Though the public has hardly noticed, one of America's biggest industries has been battling for special concessions from the Reagan administration for months, and has finally won grudging acceptance of a plan that could cost the Treasury $4 billion or more, despite the official policy of stringent austerity.

Seeking help this time is not a Lockheed or a Chrysler, but one of America's mom-and-apple-pie institutions: the savings and loan associations. They are in trouble because of high interest rates. To attract and keep deposits, they have to pay out more in interest than their old mortgages are bringing in.

For some S&Ls the troubles are so serious that some experts privately predict major failures in the months ahead if interest rates don't fall. Already, these thrift institutions are suffering unprecedented losses, more than $1 billion so far this year.

Serious S&L failures could disrupt the nation's financial markets gravely and prevent the success of the Reagan economic program, according to many economists.

Invoking those dangers, the savings and loan industry has been looking for government help for months. First it sought government intervention to cripple its newest competitor, and failed. Then it requested a direct subsidy for the Treasury, and failed. The next gambit was to seek an indirect subsidy through the federal bank insurance organizations. Another failure.

All of these efforts were rebuffed by the administration, led by senior officials committed to free-market economic policies, despite the inclinations of some Californians in President Reagan's inner circle who are close to the savings and loan industry.

The administration even overrode the concerns of the nation's chief banker, Chairman Paul A. Volcker of the Federal Reserve Board, who favored legislative action to help the S&Ls.

The new administration's aloof attitude angered the savings institutions and also aggravated Treasury Secretary Donald T. Regan's reputation as a most impolitic Cabinet officer.

The industry decided to try a back door to government aid, and this month succeeded with startling ease in winning from the Senate Finance and House Ways and Means committees tax concessions the Reagan administration has decided reluctantly that it will have to swallow if Congress adopts them.

Both committees have approved legislation to create a tax-free savings certificate that the thrigt institutions predict will attract large new deposits, easing pressure on their balance sheets.

The idea swept through Congress like a California brush fire, convincing the administration not to fight what it formally regards as "bad tax policy." The administration takes comfort from the fact that the tax-writing committees killed another tax benefit for savers, the result of which would finance most of the cost of the new break.

The Senate Finance Committee's unanimous vote for the tax-free savings certificate was incredible, one White House official said later. "This may be one of the classic lobbying efforts of recent years," he added.

The administration's free-marketeers who wanted to keep hands off the thrift industry also find solace in the fact that they held off any new government spending program to help the thrifts. The new tax break could cost the Treasury $4 billion or more, but it won't be appropriated. It's what economists call a "tax expenditure."

So, just as in the case of the informal but still substantive import quota on Japanese cars, the Reagan administration can claim ideological purity even as it accepts a more ambiguous reality.

But the tax committees have not ended the saga of the savings and loans. Many experts predict that they'll remain in trouble even if this new tax break is enacted, and if interest rates don't come down over the next six months, the thrift institutions will be assured of continued difficulties.

The S&Ls already have won the right to issue variable-rate home mortgages, which could protect them in the future against the kind of troubles they have now. Last week the Federal Home Loan Bank Board authorized S&Ls to hedge against volatile interest rates by buying futures contracts for money on the commodities exchange.

The new chief of the loan board is said to be preparing a potentially controversial set of additional nostrums to help the thrifts. But these are not short-term solutions to the problem.

The administration insists that it will stand by the thrifts, but adds that no new programs are needed. Experts in the industry and on Capitol Hill predict that the administration won't really have a policy on the thrifts until it has faced, if it does, a real crisis.

The saga so far is an intriguing tale of Washington maneuvering and posturing, special pleading and bargaining. It is a tale that has only been told in incomplete snatches in the news media, despite the billions of dollars involved and the savings industry's importance to the national economy.

It begins last year, when the thrifts first showed signs of serious suffering under the pressure of volative but persistently high interest rates. The thrifts' problem is simple: most of their assets are home mortgages, many of them issued in the days of single-digit interest rates.

But to attract new capital, these S&Ls have to offer interest rates that are competitive in today's double-digit mone;y market. Earning low interest buy paying high interest is a formula for losses.

The problems of the thrifts are aggravated in the short term by deregulation of the industry, which Congress authorized last year. Federal regulations traditionally insulated the thrifts from the free market by limiting the interest rates they could pay to depositors.

As deregulation progresses, and Congress provided up to six years to complete the process, the thrifts will have to bid increasingly for deposits against higher-paying competitors, a process that will force up the cost of funds.

The thrifts are afraid of the effect higher costs will have on profits, and generally oppose speedy deregulation, but the administration is pressing to accelerate the process as the only way to get the thrifts on a sound long-term footing.

Never before the last two years had these savings banks seen red ink on their ledgers, and even though most of them have more than enough assets to absorb losses for a long time (more than $30 billion in reserves nationwide), they got scared, and not without reason.

When the prime rate is nearly 20 percent and Treasury bills (the government's principal tool for borrowing money in the captial markets) are earning 13 ro 14 percent, the savings banks" 5 1/2 percent passbook accounts are hardly attractive investment options. A saver who has $1,000 can put that money into a money market mutual fund and earn 17 percent, without tying his money up in a 6- or 12-month certificate of deposit.

Currently, Americans are keeping more than $180 billion on deposit in savings banks accounts that earn 5 1/2 to 8 percent interest. No one knows for sure why people keep so much money in these accounts, where their savings are eroding because of high inflation, instead of investing in a more lucrative asset like a money market mutual fund.

This subject falls into an area that economists rarely study: the psychology of money. Because bankers and economists don't know why people do what they do with their money, they can rightfully worry that they might do something rash and unexpected, or, in this case, something sensible.

If, say, half the people who hold low-interest deposits in thrift institutions were to decide to move them into higher-paying bonds or money market funds, the thrift industry would collapse, setting off a national financial crisis.

The industry's big fear is of a few dramatic failures by big savings institutions that destroy public confidence and provoke huge withdrawals nationwide. At present, 263 of the 4,700 institutions supervised by the Home Loan Bank Board are officially designated as "troubled."

Industry spokesman regularly note that all deposits up to $100,000 in federally insured institutions are fully protected, even if a savings institution fails.

With thoughts like these in mind, the industry began to lobby for help from the government. Not surprisingly, an early target was the money market mutual funds, which the S&Ls rightly felt were drawing billions of dollars out of their coffers with higher interest rates.

The thrifts asked Congress to impose new requirements on the funds, including a requirement that they maintain cash reserves, as a way of holding down the interest rates they could pay investors.

The impulse to try to restrict the competition is a characteristic one for the thrifts. Though Regan, Office of Management and Budget Director David A. Stockman and other senior officials in the administration preach free-market competition as the cure to thrifts' problems, the industry generally disagrees.

Savings banks are used to a diet of cheap capital: money deposited in low-yielding savings accounts. Cheap money made possible relatively cheap home mortgages, which have been the key ingredient in American housing policy for years, and have allowed about 60 percent of Americans to live in homes they own.

But the money market funds had become so big and so popular that they had little trouble burying the idea of new controls in an avalanche of postcards to Congress from shareholders.

The thrifts then turned to other ideas for relief, particularly the hope that the government would buy up old low-yield mortgages in their portfolios as a means of simultaneously giving them new capital and removing their weakest "assets," the old mortgages.

But this and other ideas that would involve spending government money seemed out of step with both the ideology and the budget-cutting enthusiasm of the new administration.

Meanwhile, the Fed's Volcker and the heads of other regulatory agencies responsible for the thrift institutions began to look for their own solutions to the problems of the thrifts.

By the beginning of 1981 they were concerned that more had to be done to assure both the public and the financial industry that the responsible government agencies would be able to protect depositors and savings banks in these troubled times.

The regulators invited officials of the newly reconstituted Treasury Department to take part in a joint effort to write legislation to help the thrifts.

The Treasury sent representatives but they refused to participate in the drafting, a reticence that signaled their unwillingness to commit the new administration to any legislative remedies. Secretary Regan told Volcker that the regulators should write the best bill they could, but gave no promise to support it, according to a senior Treasury official.

The regulators made three proposals: that banks and healthy S&Ls be permitted to merge across state lines with ailing thrift institutions; that the Federal Deposit Insurance Corp. be allowed to inject funds into banks in trouble, and that the Federal Savings and Loan Insurance Corp.'s line of credit with the Treasury be increased from $750 million to $3 billion to help protect depositors in failing institutions.

Completion of the regulators' draft bill set off a contest inside the administration over how policy toward the thrifts would be decided.

The issue fell into the jurisdiction of the Cabinet Council on Economic Affairs, one of the Cabinet subcommittees that have become important forums for resolving policy matters in this administration.

The members of this council include the secretaries of treasury, commerce and housing and urban development, the budget director, the chairman of the Council of Economic Advisers and the assistant to the president for policy development.

Within this group, Regan and Stockman, and the officials who represented them on this issue, had a strong ideological inclination to resist any sort of bailout for the thrift institutions. But those inclinations did not have a free run.

Friends of the savings and loan industry are also influential in the Reagan administration. One of them is Edwin J. Gray, director of the White House Office of Policy Development and a former officer of a California savings and loan.

More important is another Edwin in the White House: Edwin Meese III, counselor to the president, also close to California savings and loan executives such as Gordon Luce, president of San Diego Federal Savings and Loan, who was a member of Reagan's state cabinet in Sacramento.

At one point in May Meese and White House chief of staff James A. Baker III attended a meeting of the Cabinet Council on Economic Affairs, one participant disclosed. According to this source, Meese and Baker took this unusual step to prevent Stockman and Regan from making the decision both sought: to tell the savings institutions that they would have to cope without new government assistance.

The free-marketeers were insistent, however. As one of the players put it later, they refused to be moved by the political strategy of the thrift industry, which he described as "to scream as loud as you possibly can, so that you will shake the rafters."

A lot of people, said this senior official at the Treasury, "don't understand finance . . . and they are susceptible to being frightened, especially if long-faced, sober types are parading corpses in front of you."

Those hypothetical corpses of course, belonged to savings institutions that might fail, possibly setting off a panic and thus a national financial crisis. The specter of disaster has always been the industry's strongest bargaining card, not least because few politicians have the courage to tell the bankers that their fears are misplaced.

However, there are limits on the methods and the drama with which this specter can be invoked. It is almost a taboo among both bankers and federal regulators to speak publicly about possible bank or thrift failures, for fear of sparking panic. (Most federally chartered banks are much less tied to home mortgages than are S&Ls, and are thus much healthier now, though small, rural banks are also having difficulties.) The preferred industry tactic is to speak ominously in private but reassuringly in public.

The preferred government posture, from the industry's point of view, is one of forthcoming sympathy. Bankers look to Washington for words and deeds that will calm the marketplace, particularly those faithful depositors who keep their money in passbook accounts, while they seek concrete benefits that will improve their balance sheets. Luce of San Diego Federal, for example, said the government should be making "statements that would inspire more confidence" in the thrift industry.

It is on this count that the industry seems most displeased with the administration, particularly its Treasury Department. Members of the House and Senate have picked up this refrain. "Either Secretary Regan is dense to their plight," said one Republican close to the Senate leadership, speaking of the thrift institutions, "or he doesn't care . . . He is as unastute politically as any treasury secretary I've seen in a while."

Regan's problems were encapsulated in an interview he gave to the Los Angeles Times at the end of May. "Well," the secretary said, "the thrifts are losing money. So what? Every time a company loses money, is the federal government supposed to go in and make it whole? I don't see that."

Regan's "so what?" was interpreted in the industry as the functional equivalent of "drop dead," with predictable results. Sen. Jake Garn (R-Utah), chairman of the Senate Banking Committee, recalled in an interview that he told Regan: "Just those two words have destroyed your image as wanting to help the thrifts."

As one senior administration official sympathetic to the thrifts put it, industry leaders developed a case of "sheer frustraton" with the Treasury and, by extension, the entire administration, which it had expected to be much more sympathetic than its Democratic predecessor.

On may 30 the effort Volcker had orchestrated to produce a "regulators' bill" to help the thrifts collapsed. Regan wrote a letter to the chairmen of the House and Senate Banking committees announcing that the administration would be "neutral" on the proposal to allow interstate bank mergers, but would oppose the other ideas that could involve additional outlays of federal funds.

The decision to send that letter represented a victory for Regan and Stockman over others in the administration who wanted to offer more comfort to the thrifts. The way the matter was handled did nothing to ease already strained relations between Volcker and the administration, according to knowledgable sources.

Richard Pratt, the administration's choice to the new head of the Home Loan Bank Board, also abandoned the regulators' bill, though his predecessor and staff had worked on it and endorsed it.

And the industry, which always feared the interstate merger provision as an invitation to takeovers by giant bank holding companies, was also happy to be able to oppose it. Rep. Fernand J. St. Germain (D-R.I.), chairman of the House Banking Committee, dropped the whole package.

A reporter making the rounds of administration, congressional and industry sources during early June got the impression that the free-marketeers in the Treasury and White House had won at least the first important skirmish on the S&L issue, which was just what the free marketers thought too. But they had miscalculated the political atmosphere.

This became evident on June 22, when the Senate Finance Committee unanimously adopted a new section for its tax bill to create tax-free savings certificates in S&Ls, banks and credit unions. This was the industry's riposte to the indifference it felt from the administration, and it struck hard.

According to members of Congress, the Senate committee's vote, and a similar one subsequently in the House Ways and Means Committee, was a natural politicians' reaction to anxieties about the politically popular thrift industry.

"It was obviously necessary" to authorize the tax-free accounts, St Germain said. Sen. Bill Bradley (D-N.J.), a member of the Finance Committee, said that, given the climate, the thrifts could have gotten more out of the committee than just this tax break, which would go equally to banks and credit unions in the Senate bill.

The tax measure was hardly welcome to the administration's free-marketeers, but if they every wanted to try to fight it, that idea was quickly rejected. Friends of the S&Ls inside the White House concluded that the political momentum behind the tax break was unstoppable, and that accepting the tax-free savings accounts would be a relatively cheap way of signaling some willingness to support the thrift industry.

William B. O'Connell, executive vice president of the U.S. League of Savings Associations, said in an interview that he thought Treasury had tried to block or limit the "all savers" proposal, as the industry called it, but realized it couldn't be stopped.

However, there is no guarantee that tax-free savings certificates will solve the thrift institutions' problems. Many experts say that depositors may just move the funds they already have in thrift institutions into the new certificates, a shift that will do little, if anything, for the thrifts.

Others speculate that if banks and credit unions are permitted to issue the tax-free certificates (the Senate bill allows for this, the House version may not), they could get most of the benefit.

One key congreesional aide said the tax-free certificate was a gimmick promoted by the savings associations league, a Washington-based trade association, as a means of demonstrating to its members that it could win something for the industry, but which won't prove very helpful, and could actually harm the institutions.

"Approving this will take all the heat off" Congress to do anything more for the thrifts, this aide said, diminishing the chance that potentially more-helpful legal changes will be adopted later.

And there is little question that the industry will remain in trouble, especially if interest rates stay high. Every expert and banker interviewed for this article agreed that the only solution to the industry's problems is lower interest rates generally.

Alan Greenspan, a conservative economist who is close to the administration, said in an interview that if rates remain high for another six months the result will be "very unstable institutions" next year, both thrifts and small commercial banks.

And if Treasury bill rates rise from today's 14 percent to as much as 20 percent, an unlikely development, but one some Wall Street bears fear, "you'll have the dissolution of the industry somewhere down the road," Greenspan said. "The system will just liquidate."

His economic consulting firm, Townsend-Greenspan, recently published a study of the thrift industry concluding that "short of a major and immediate interst rate decline," the thrifts will experience " a major and immediate interest rate decline," the thrifts will experience "a major acceleration in losses which could dwarf anything seen previously in the history of these institutions."

Interest rates slightly below current levels through the end of next year would produce industrywide losses of $5.5 billion this year and $7 billion next, Townsend-Greenspan predicted. That would leave the industry with an aggregate net worth of nearly $25 billion. However, if rates fell 3 1/2 percent, the firm concluded, the industry would go back into the black.