There is one thing that backers of federal aid for Chrysler Corp. agree on. They are all for the free enterprise system, but . . .

But Chrysler pays black employes $800 million a year, which is 1 percent of all the personal income of blacks in this country. So the NAACP has passed a resolution in favor of aid and members of the Congressional Black Caucus, including D.C. Delegate Walter E. Fauntroy, have indicated they want to help the company.

But 18,900 companies, including such giants as Goodyear Tire and Bendix, sell $7.9 billion in parts and services to to Chrysler. So hundreds of firms are urging support for the auto maker.

But chrysler provides jobs for blue-collar workers, and sales for small businesses. So the United Auto Workers and the National Automobile Dealers Association are going all-out to lobby Congress to help.

Though it may be a month before the House votes on an administration backed plan to provide Chrysler with $1.5 billion in federal loan guarantees, these pragmatic "buts" have become crucial factors in the backstage politicking.

And they helped Chrysler's supporters build a strong, early coalition.

Rep. William M. Brodhead (D-Mich.) has written every member of the New York State Delegation, drawing these colleagues' attention to parallels between Chrysler's present plight and New York City's when it sought loans in 1975.

"Now's the time to cash our chits from the New York delegation. They owe us something," Brodhead told fellow legislators at a meeting of the Michigan delegation in October.

Members of the Michigan House group also said that the need to rally broad support for Chrysler later this year was considered in connection with an Oct. 23 floor vote on a major sugar price support measure.

"The link-up there was pretty explicit," said Brodhead, who netherless voted against the sugar bill.

Brodhead said the linkage was drawn by another Michigan Democrat, Bob Traxler, whose district grows sugar beets and who is a member of the House sugar caucus.

"He [Traxler] said it would be helpful if we could help people out who wanted a sugar bill," said Brodhead.

The administration-backed measure, which would have increased sugar price supports and provided direct subsidy payments to sugar farmers, was defeated 249 to 158. Opponents claimed it would have cost consumers $400 million a year.

The Michigan delegation voted 10 to 7 for the sugar bill, mustering four more votes in favor than in 1978.

Rep. James J. Blanchard (D-Mich.), who has been spearheading legislative effort on behalf of Chrysler in the Michigan delegation, voted in favor. Before the vote, he had been reported by sugar lobbyists as leaning against the bill. Blanchard said this week that there was no connection between his vote and the Chrysler issue.

Another Michigan Democrat, Lucien N. Nedzi, who voted against higher sugar supports in 1978, voted for the 1979 bill.

"I had heard the argument about Chrysler made, but I honestly can't tell you whether it was a factor" in supporting the sugar measure, he said.

The Chrysler relief plan is currently being opposed by lobbyists for Ralph Nader, who say the plan would "duplicate the British experience," and the National Association of Manufacturers, which is fighting government regulation.

"We can hardly support this bill and then call for government to get off our backs," said an NAM spokesman.

Conservatives in Congress who are philosophically opposed to government aid to industry say they have been isolated by the scramble to join the rescue operation.

Rep. David A. Stockman (R-Mich.), who opposes the relief plan, says he has been under strong pressure from the Michigan delegation to change his position.

"There's a feeling on their part that you have a swallow your principles and join ranks to help the state," says Stockman, who says he prefers a program of extensive retraining and adjustment assistance for Chrysler workers who lost their jobs.

Brodhead said yesterday that "if we can't make a good case, all the lobbying and vote trading won't work."

However, practical politics thus far has played a major part in the lobbying effort.

The Michigan delegation has been the focal point for the lobbying effort since last summer. Chrysler operations and jobs are heavily concerntrated in that state, in which the auto company has 58 percent of its work force and spends about $2.5 billion a year.

To aid its campaign in Washington, Chrysler has retained William Timmons, a senior White House adviser under Presidents Nixon and Ford; two former congressmen, Garry Brown of Michigan and Joe Waggonner of Louisiana; and attorney Thomas Hale Boggs, son of the late House Majority Leader Hale Boggs.

But Michigan and Chrysler interests have picked up broad support as well from labor and other groups with a strong interest in keeping Chrysler solvent.

The United Auto Workers and Chrysler, as well as some chrysler suppliers, have been working together in Washington in devising a strategy for building a coalition on Capitol Hill.

"A profit-making corporation has no claim on the government for help," acknowledged a labor union official. "But in this case there are scores of communities and thousands of workers who need help."

One-third of the company's blue-collar work force and one-tenth of its white collar employes are members of minority groups, mostly blacks.

Fauntroy plans to cosponsor aid legislation being introduced by Michigan's Blanchard.

"The nation has a moral obligation to support this plan," said a Michigan congressional aid. "It's fine for [columnist] George Will to make hypothetical statements about keeping the government out of the economy, but in this case families are at stake and it looks different from that angle."