Like millions of Americans, Elizabeth Slany's savings are federally insured up to $100,000. It's a guarantee from the U.S. government that not a penny could be lost or frozen no matter how shaky the balance sheet of her savings and loan.

But Slany found little solace in Uncle Sam's promise when federal regulators announced last month that they are seeking a buyer for her S&L -- National Permanent Bank, Washington's second-largest thrift -- as a way to restore it to financial health. Instead, the 57-year-old Chevy Chase resident started to think of moving her savings into a bank or the stock market.

"Federal insurance doesn't make me feel more secure," Slany said. "I know about the magnitude of problems in the S&L industry."

The financial plight facing one-third of the nation's 3,200 thrift institutions is straining more than the Federal Savings and Loan Insurance Corp., the federal agency that insures S&Ls. Industry experts warn that, as the problem drags on, depositors are losing faith in FSLIC and, as a result, in the savings and loan system.

"The danger to the thrift industry is the perception of risk, rather than the reality of it," said Allan Bortel, S&L analyst at Shearson Lehman Brothers Inc. "The amount of money in a federal insurance agency is not important. The perceived confidence -- that what's important."

With such concerns in mind, the House and Senate banking committees begin a series of hearings today on the health of the nation's deposit insurance system. The aim is to determine the extent of the problem and to hear suggestions for fixing it from government executives and industry leaders.

Proposed remedies range from charging higher insurance premiums to speeding up interstate banking and the blurring of distinctions among banks, savings and loans, securities brokers, retailers and a host of other industries. Because 1986 is an election year, however, the likelihood that Congress will adopt any of the proposals this year is small, industry and government leaders say.

"But you never know," said Mark F. Clark, a spokesman for the U.S. League of Savings Institutions, a powerful lobby group for the S&L industry.

Regulators and S&L executives alike say they are pushing lawmakers to bolster public confidence by finding a long-term solution to weed out the sickest S&Ls and revitalize those worth saving.

But prospects for action are no more likely this year than during the last three, when disagreement among regulators, the White House and industry leaders blocked legislation. The result is that many thrift industry leaders say they are resigned to another year of rising business costs as more customers become unwilling to keep money in institutions perceived as risky or will do so only if lured by higher rates.

Despite the slim hope lawmakers soon will pass major legislation, they will get an earful of ideas during the next few weeks on ways to boost FSLIC reserves which, at $6.06 billion, fall short by as much as $5 billion from potential need, according to a recent report by the General Accounting Office. The fund's unmet costs could double each year if no action is taken, say officials at GAO, a watchdog arm of Congress.

The Federal Home Loan Bank Board, which regulates thrifts, runs FSLIC.

By federal regulatory rules, many thrifts are too shaky to stay in operation and should be merged or closed. But FSLIC, drained from five years of record S&L failures, cannot afford to take action. Instead, the bank board and Congress have adopted a series of stop-gap measures since 1980 to prop up the value of the institutions and defer closings while a long-term answer is sought.

Here is what is likely to be proposed at the hearings that start today:

*The U.S. league says that it favors letting ailing thrifts heal under current market conditions, which, with stable, low inflation are favorable to the industry, league officials say. It also favors allowing FSLIC to borrow from the 12 regional Home Loan Banks.

Wall Street analysts such as Bortel at Shearson oppose this solution, saying it would weaken the strong credit rating of the Home Loan Banks. The banks borrow money on behalf of the nation's S&Ls.

*Officials at the Federal Home Loan Bank Board say the agency is considering tightening S&Ls' operating rules, including raising net worth requirements. In the early 1980s, the required net worth was lowered to 3 percent of assets from 6 percent so that many thrifts could meet federal operating rules and keep their doors open.

The bank board says it also is considering a risk-based net worth policy that would tie reserves to the soundness of institutions' activities. The policy would be part of an effort by the bank board to clamp down on thrifts that hold few, if any, home loans but have invested heavily in speculative activities such as real estate development. Many such federally insured institutions are in Texas, Florida and Louisiana.

Bank Board Chairman Edwin J. Gray told Congress last summer that another alternative is to charge FSLIC-backed thrifts with a one-time, 1 percent levy on deposits. Many officials within industry, government and the bank board itself, however, protest that a levy would push hundreds of S&Ls to defect from FSLIC and join the Federal Deposit Insurance Corp., the federal insurer of the nation's banks. That would leave FSLIC with even fewer healthy funding sources.

Gray has told Congress that "a fundamental cornerstone of the bank board's policy is to seek acquirers of failing and failed thrift institutions from wide sectors of the marketplace . . . including insurance companies." But in practice, the board has made most awards to healthy banks and S&Ls and never to an insurance company, bank board spokesmen say.

*The U.S. Treasury favors encouraging FSLIC to continue to be more active in getting bids for ailing thrifts -- and actual awards -- to a wider variety of industries, including insurance and other firms connected with securities activity. Treasury Undersecretary George Gould is expected to make such a proposal at Senate hearings today.

Bitterly opposed by the U.S. league, the trend toward opening the bidding process to many types of industry raises broader questions, particularly concerning interstate banking and the possible blurring of any distinction between banks and thrifts.

But unlike the league, the National Council of Savings Institutions, a lobby group that represents the larger thrift institutions in the industry, wants to open bids for sick thrifts to securities and insurance companies.

"The industry needs the capital and FSLIC needs to take care of its problems at lower cost," said council spokesman George Hanc.