The Carter administration this past week shouldered the burden of the U.S. auto industry, accepting a share of the responsibility for its survival.

The White House "summit" meeting Wednesday between President Carter and the industry's leaders was only a footnote to the big news on the auto front, the approval of the Chrysler bail-out plan eight days ago.

But the meeting symbolized an important change in the relationship between U.S. business and the Carter administration, according to participants from both sides.

President Carter told the industry and union leaders Wednesday that years of "poor-mouthing" the U.S. auto industry had hurt the public's confidence in its product. Too many motorists regard American cars as lemons, he suggested.

"We're going to cooperate to help build it up," Carter promised his audience.

The President promised to take steps to make more credit available to car buyers, to cure an unintended drought in auto loans. In the next six weeks, government and industry officials will see what else can be done to deal with the automakers' problems with imports, regulation and financing. No commitments have been made yet.

Cooperation between government and business is nothing new. For years, Washington has helped shelter parts of the oil industry and much of the steel and maritime industries.

But it hasn't been customary for presidents to draw the link between an industry's interests and the government's so bluntly and publicly. The industry leaders have struck up the old refrain: "What's good for General Motors -- and Ford, Chrysler and American Motors -- is good for the U.S.A.," and one could almost hear the Carter administration singing "amen."

The shorthand phrase for such a relationship is an "industrial policy." It works in Japan, because that country is smaller, its national goals are more obvious, and accommodation is a practiced way of life.

It's true that what hurts the auto industry damages the economy generally, as layoffs in auto plants are followed by more unemployment among people who make auto glass, vinyl upholstery, tires and parts. But giving Detroit the help it wants can cause other serious problems elsewhere. A look at the wish list the auto leaders brought with them to Washington makes the point.

Chrysler Corp. President Lee Iacocca called for a $1,500 tax credit to reward people who buy energy-conserving compacts and subcompacts, reasoning that consumers who can get credits for installing storm windows should also be able to get them for swapping gas-guzzlers for a fuel-efficient compacts.

But the cost to the government in lost tax revenues from Chrysler customers alone could equal $1.5 billion in 1980-81, doubling the size of the loan guarantee.

That won't fly at a time when Congress and the White House are straining to balance the federal budget.

Philip Caldwell, Ford's chairman, trained his sights on Japan, which has poured imports into the United States to meet the sudden explosion in demand for small, high-mileage cars -- a demand that Ford and Chrysler, in particular, were not equipped to satisfy.

Ford's appeal is wrapped in the American flag. The auto market is a vital national resource, he told reporters, and the government should be protecting it. Why should Japan's auto plants be running on overtime to supply cars for the United States while U.S. plants are closing down? he asked.

The short answer is that the idle U.S. plants were making big cars that American consumers didn't want. Caldwell responds that the abrupt change in consumer attitudes was caused by the overthrow of the shah in Iran and the gasoline crunch that followed, events that Ford's planning hadn't anticipated.

What Ford wants is a short-run, unofficial lid on Japanese imports to give U.S. automakers a chance to regroup and retool plants to make more small cars. Ultimately, he would like to see a stiff "content rule" applied requiring three-quarters of the parts of a foreign import to be made in the U.S. and assembled here. That requirement would compel Japan and other foreign auto companies to establish more production plants in the United States.

But such a single-shot approach overlooks the much broader range of tough trade problems, government officials note.

A critical issue centers on U.S. demands that Japan let American electronics companies bid on contracts to supply sophisticated equipment to Japan's telephone and communications monopoly. The multilateral trade agreement signed by both countries calls for fairer treatment in government procurement practices. So far, however, Japan is talking about accepting bids on cement telephone poles, for example, rather than electronic gear U.S. firms want to sell.

What if Japan is willing to give ground on autos, or communications equipment, but not both? trade officials ask. An industrial policy presumably would help Washington officials deal with trade-offs like that, but there is no such policy now, and, given the lack of consensus in the country, there isn't likely to be one in the foreseeable future.

There isn't a consensus within top levels of the Carter administration, for example, on the future regulation of the industry. Critical decisions lie ahead on increasing the miles-per-gallon fuel economy of autos in the 1990s, and in determining the health risks from diesel exhaust. The shorter the arm's-length relationship between the government regulators and the industry, the trickier those decisions become.

Recognizing these dilemmas, White House officials say they intend at least to increase give-and-take discussions and negotiations between the government and the industry to see what help can be offered without compromising important national goals -- highway safety, auto emissions cntrols, for instance.

A cooperative automotive research program between administration officials and the industry is under way, aimed at increasing basic research on new materials, auto design, motor controls systems, and other technological issues for the future.

These effort are long-range; however, they won't add to the safety net that Chrysler and, perhaps Ford, will need to get through the next year.

Even with $1.5 billion in federally guaranteed loans, Chrysler is still in serious trouble, some analysts believe. It is now expected to lose $1.1 billion this year, according to estimates by Treasury Department analysts, and its plight continues to generate damaging publicity. Chrysler's share of the U.S. car market has dropped 1-1/2 percentage points below the meager 9.8 percent share of a year ago, according to a critical study by the Republican staff of the Senate Budget Committee.

"We believe the risk is high that Chrysler will not achieve its profit predictions, and, in fact, will not return to profitability," the Republican analysts said.

The staff of the government's Chrysler loan guarantee board, while concluding that Chrysler has a "reasonable" chance of survival, warned that this judgment was "subject to a high degree of risk, because Chrysler can be expected to be only marginally profitable over the 1981-1983 period."

And Chrysler may not be the only company in need of help.

Ford Motor Co.'s sales in the first 10 days of May were more than 50 percent below the figure a year ago, and the company is facing potential losses of over $1.5 billion this year from its domestic operations, according to some forecasts. Like Chrysler, it gambled that the love affair between American motorists and big cars was not over.

Ford officials now believe it will take several years for the company's domestic operations to recover, even with substantial help from Ford's successful overseas operations.