In a certain symbolic way. Jimmy Carter's war against rising hospital costs began and ended at St. Luke's Hospital in Bethlehem, Pa. the steel-making city.

There are larger and more prestigious institutions among America's 7,000 hospitals, but St. Luke's is as typical as the next in one important respect.

It is a special interest.

The people who run St. Luke's don't see it quite that way. Like other hospitals, it enjoys a special respect as the healer: its fortunes are overseen by pillars of the community.

The 33-member board includes doctors, bankers, businessmen, an Episcopal bishop, several college presidents, homemakers, labor and industry people and even a member of Congress, Democrat Fred B. Rooney.

They oversee a medical staff of serveral hundred, more than 1,000 employes and even more volunteer workers - the "St. Luke's family," as President Richard L. Stock calls it.

But like hospitals everywhere, St. Luke's is riding a runaway cost juggernaut. An average day's stay there in 1973 cost $34.29. Today it costs $153.79 - and the end is not in sight.

When President Carter asked Congress in early 1977 to put a mandatory limit on hospital cost increases - it would have been about 9 percent a year - the St. Lukes of America mobilized themselves into a potent hobbying force.

As much say, as oil companies or labor unions, farmers or environmentalists, hospitals have a concern about the laws and regulations that govern their freedom and their income.

Carter has identified the hospitals and the doctors who work in them as "an extraordinary monopoly." Its dimensions make it awesome: it is one of the country's largest industries, generating about $60 billion a year and employing 24 million workers.

The evolution of the political potency of the hospital-medical industry is not unlike that of a multitude of other special interests that have descended with abandon on Washington.

In this era of more federal involvement in everyday affairs - more regulation, more restriction, more paper-work - they want protection.

To get it, they hire lobbyists to tell their story. They contribute handsomely to congressional campaigns. They blitz Congress with mail and make visits to express their opinions and seek support.

It is not a question of venality or the buying of votes. Rather, it is a reflection of the conglomeration of special interests that layer society today.

St. Luke's had less of a problem in making its point to the congressman from Bethlehem. Rooney, like fellow board members, thought Carter's cost-containment bill was "unworkable." He and eight other Democrats helped kill the bill in the House Commerce Committee last July.

But the task was far more complicated for the rest of the hospitals and doctors' groups around the country. They knew, when the president sent his bill to Congress, that they had a fight on their hands and that they had to get organized.

"The bill was so clearly a threat to hospital care and so clearly a rationing of health care that it unified all the elements of the industry," said Dr. James Sammons, executive vice president of the American Medical Association.

The AMA is given to that kind of overstatement, but it works. The threat Sammons talked about got the top brass of the AMA and their confederates fromt he American Hospital Association and the Federation fo American Hospitals thinking alike.

The difficulty, however, was marshaling the force of their members. "Most of these people really aren't political," said Michael Bromberg, executive director of the FAH. "Hospital administrators are politically naive, the trustees aren't active . . . They sit on four or five boards and they can't keep up."

Bromberg, Sammons and J. Alexander Mcmahon, presidend of the AHA, went to work early last year to arouse the force. They had some advantages before they began.

For one thing, Congress doesn't like to challenge the medical establishment - health is too important to be politicized, one might argue. For another, there was an anti-regulatory mood in Congress and the administration's bill was not assured of a warm reception.

More important, perhaps, were the resources, the membership and the ready-made network of contacts the three groups shared in every corner of the country.

The AMA is one of the most influential, best-known and wealthiest of all special-interest groups. It has slightly more than 200,000 members - about half of the country's doctors - and yearly expenses of around $50 million. Part of the $1.5 million the AMA spends for lobbying goes toward a large Washington office, which keeps tabs on legislation and governmental actions.

The AHA, based in Chicago like the AMA, represents 6,400 hospital and nursing homes and has some 27,000 individual members on its rolls. A staff of 30 in Washington watches Congress and the federal government.

The FAH represents 780 of the 986 investor-owned hospitals in the country, operates on a $1.1 million annual budget and, from its headquarters here, monitors federal and state health-care activities.

The three organizations' ability to activate their networks, their knowledge of which magic buttons produce a congressional response, and the campaign contributions they can make give them power.

Bromberg, whose skill as a persuasive lobbylist is conceded even by his adversaries, found an irony as the cost-containment battle unfolded. He thought the hospitals' biggest unifying spark came from Joseph A. Califano Jr., the secretary of health, education and welfare.

"The White House was hell-bent on the Cabinet system and they weren't going to interfere with Califano," he said. "Califano antagonized 7,000 hospitals and their boards with his criticisms, he went on a rampage and riled us up and got us together for the first time in 13 years."

After that, the industry's battle plan was simplified. First, it laid out a strategy for targeting key committee members and torpedoing the bill. Second, it made certain that campaigning legislators got financial assistance.

Roughly, it worked this way:

Hospital administrators came to Washington to meet with legislators. Hospital people called on lawmakers in their home districts. Visits were timed to coincide with votes on key amendments in the congressional committees.

This kind of blanket voverage, with follow-up calls and visits as the bills moved through subcommittee and committee, was orchestrated in daily strategy conferences.

All it was blanket coverage. In some cases, by the time Carter or Califano called a legislator to seek his support, he already had seen hospital lobbyists three or four times. Once, when Vice President Mondale called Rep. James J. Florio (D.N.J.), Bromberg was sitting in the office.

There was another important wrinkle in the industry's effort. They concentrated on the House. The House is more conservative than the Senate, access to members is greater, staff membes tend to have less sway over legislation and responsiveness to district problems may be higher than that of senators representing an entire state.

That emphasis paid off. The bill fell into a fatal time warp in the House, delayed by amendments, pressured off the calendar by other bills and subjected to debate that gave the hospitals more maneuvering time.

"That is the first one of those [delays] that we hadn't planted. If they had called for a vote after two weeks, we would have lost," Bromberg said.

If access to a lawmaker's mind is the name of this game, then campaign money is the grease on the hinges of the congressional doors. Through their political action committees, the AMA and the FAH made ample grease available.

The AMA is the country's largest special-interest giver. More that $3.2 million of the doctors' money went to congressional candidates in 1974 and 1976. The FAH contributes substantially less, but spreads its money among lawmakers who help on health measures. The AMA has just decided to set up a campaign fund.

The big money, of course, goes to campaigns. But the medical lobby has another impact by paying legislators for speeches they make at conventions and meetings.

The sharpest example of theat approach: Rep. David E. Satterfield III (D-Va.), who opposed Carter's bill in the Commerce Committee. He received no campaign money from the AMA. But since 1975, according to House records, he has received more than $9,000 in fees and expenses for speeches to medical groups.

On Ways and Means, Rep. Dan Rostenkowski (D-III.), health subcommittee chairman, got at least $13,500 in campaign and speech money from medical interests in four years. He opposed mandatory cost controls.

A Common Cause study showed that 11 members of his subcommittee received $73,462 from the AMA and the FAH in their 1974 and 1976 campaigns.

The subcommittee, by a 7-to-6 vote, approved a voluntary, instead of mandatory, containment bill that pleased the hospitals only a little more than Carter's bill.

Rep. Harold E. Ford (D-Tenn.) delivered the crucial seventh vote after lengthy hemming and hawing. He was under enormous pressure from both sides. Carter, Rostenkowski and House Speaker Thomas P. (Trip) O'Neill Jr. (D-Mass) werer pushing against a medical lobby that has provided a fifth of Ford's current campaign fund. Covering his bases, Ford reserved the right to oppose the bill later.

Another Common Cause study found that the AMA had given $101,259 to Commerce Committee members between 1976 and raid-1978. The bulk of that - about $85,150 - went to 19 members who voted against Carter. The bill lost, 22 to 21.

"The AMA's political money buys enormous clout in Congress," said Fred Wertheimer, senior vice president of Common Cause. "It obviously made a difference in the one-vote defeat of the administration's proposal."

A look at Federal Election Commission reports is more suggestive. Consider the case of Rep. James D. Santini (D-Nev.), who turned out to be one of the hospitals' principal allies on Commerce. Timing, it seems, is basic.

Santini rejects the notion that his opposition - including an amendment that would have gutted the Carter bill - was based on anything but the merits of the case. He said he opposed the bill on principle. It was unfair, it meant more regulation and it wouldn't work, he said.

Yet in the two weeks following his introduction of his amendment (it lost 22 to 20), Nevada physicians gave him $6,950. According to FEC records, Santini through August had collected $16,900 from medical interests this year. Almost all of it was contributed during the vital six weeks that the legislation was before the Commerce Committee.

Texas Rep. Bob Krueger was another of the Democrats on the committee who opposed Carter's bill. He received at lease three presonal telephone appeals from the president for his vote. He has accepted more that $17,000 from the AMA in three years.

Those money alliances, if they mean anything, work the other way as well. Organized labor wanted a wage exemption - called a pass-through - put into the president's bill. Rep. Bob Eckhardt (D-Tex.) introduced the amendment and it passed, 15 to 13.

Eleven of the 15 to vote for it had received a total of $61,249 from political action committees of the AFL-CIO, which was pushing the amendment, between 1975 and mid-1978. Among the 15 was Santini, who received $4,999 from labor. Only one of the 13 opponents got any labor money during that period - $4,513 to Rep. Timothy E. Wirth (D-Colo.).

"Contributions have no effect," said the AMA's Sammons. "The money helps elect people whose basic philosophy is being indentified. They are inclined to sit and talk with you - in no way are you buying votes."

Th real meaning of access showed up during the dying hours of the 95th Congress, after the administration activity got modified, voluntary cost-control bill through the Senate.

The hospitals had two simple ways to move and they did both to perfection.All it took was some telegrams, some telephone calls, some visits - punching the right keys on the great console to get the right response.

First, the lobby got 40 House members to write to the Rules Committee, demanding to testify if the panel decided to consider the Senate bill for floor action. The threat of prolonged controversy stopped the committee.

Then they made certain that enough of their sympathizers on the Ways and Means Committee would be around to prevent the bill from moving from there to the floor for a final vote if it were tired.

The House never got a chance to vote before it ajourned. Nine days later, President Carter outlined his new anti-inflation program on television. He asked Americans to write to their members of Congress to put controls on hospital costs.

It was too little, too late.