But their cooperation will be put to the test as the sides square off over how to divide the profits of Detroit’s unexpectedly swift revival.

After a period of plunging sales, bankruptcies and government bailouts, the union is hoping to regain some of its lost jobs, reopen closed factories, and increase the pay of its 111,000 members, some of whom are being paid half as much for entry-level jobs as other workers under a two-tier wage arrangement.

But those goals run against the priorities of Detroit’s Big Three automakers, who want to hold the line on costs and further close the gap in productivity with foreign-owned factories in the United States, which employ much cheaper nonunion workers.

And while contract negotiations are always prickly, this round has a particularly prominent backdrop: the long shadow of the Obama administration, which bailed out both General Motors and Chrysler and shepherded the automakers through Chapter 11.

As part of the bailouts, the U.A.W. agreed to no-strike clauses at both companies and to submit to arbitration in the event that a contract could not be reached.

That leaves Ford, the most successful of the three, as the only possible strike target should the talks fall apart. But the U.A.W. benefited greatly from the federal intervention, and Ford has been hailed by consumers for surviving the recession without financial help from taxpayers.

For the union to strike Ford or enter a contentious arbitration process could reignite debate over the bailouts and prove politically embarrassing to President Obama as he readies next year’s re-election campaign.

Bob King, the union’s president, said in an interview that he was “morally and legally” bound to get the best deal possible for his membership, regardless of the political consequences. “But if we end up with a strike or arbitration,” he acknowledged, “I’d feel like I failed in many ways.”

The union’s four-year contracts with G.M., Ford and Chrysler expire in mid-September. Indications are that the U.A.W. will be aggressively seeking better profit-sharing, job guarantees, and wage increases for lower-paid, entry-level workers.

“Our members have sacrificed a lot,” Mr. King said. “We’re trying to figure out a path that gives members more income but doesn’t disadvantage the companies.”

All three automakers are making money and expanding sales. But they are loath to do anything that hurts their newfound competitiveness or adds costs to their streamlined manufacturing operations. The Big Three earned nearly $6 billion in combined profits during the first quarter of this year, and paid sizable profit-sharing checks this spring based on their 2010 results.

“We all know that there are things we can’t do to go back to how we were,” said Cathy Clegg, head of G.M. labor relations, during an appearance Monday at a truck plant in Flint, Mich. “We need to see a pretty healthy market recovery before we start turning factories back on.”

All three companies have drastically cut production and jobs in recent years to better match their smaller market shares. The U.A.W. currently has less than half the number of employees at G.M., Ford and Chrysler than just five years ago.

The pain of losing so many jobs is still fresh in the minds of the surviving workers, said Mr. King, who was elected president last year after previously running the U.A.W.’s Ford division.

“They want stability,” he said. “They want to know they’ll be working next week and next year, and that they will be able to send their kids to college.”

But while preserving jobs is paramount, Mr. King said that workers deserved a bigger share of the economic benefits of Detroit’s turnaround.

While Mr. King does not expect across-the-board wage increases, he said the automakers should improve their profit-sharing formulas, something some auto executives have indicated a willingness to consider. He added that new entry-level workers, who are paid about $15 an hour compared with $28 for regular U.A.W. members, deserve pay increases in the new contract.

“I don’t think you should be working in the auto industry at poverty-level wages when the companies are doing well,” he said.

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