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Under the jobs bank program, workers receive up to 95 percent of their pay during a layoff. The arrangement has been both a public black eye to the union as national unemployment has soared, as well as an embarrassment to the Big Three managers who agreed to it many years ago.

Mr. Gettelfinger said the bank now assists 3,500 workers, drastically down from just three years ago, but conceded that seems to have little effect on the public.

“Jobs bank has become a sound bite that people use to beat us up,” he said.

The automakers did win qualified praise from both the White House and President-elect Barack Obama on Wednesday for detailed programs they submitted to Congress on Tuesday on how much money they needed, how it would be spent, what cuts they would make and how taxpayers would benefit.

Lawmakers of both parties had slammed the companies last month for what they saw as vague restructuring blueprints that failed to acknowledge the companies’ own marketing and production mistakes.

“It appears, based on reports that we’ve seen, that this time now the executives from these automakers are putting forward a more serious set of plans,” Mr. Obama told reporters at a news conference in Chicago.

But the president-elect said he would monitor hearings before the Senate Banking, Housing and Urban Affairs Committee on Thursday and the House Financial Services Committee on Friday before passing final judgment.

The White House expressed some openness to the automakers’ proposal, but also pointedly did not go so far as House Speaker Nancy Pelosi’s statement Tuesday that bankruptcy for any of the three leading U.S. carmakers is “not an option.”

“We don’t want anybody to be negatively affected by a bankruptcy, but sometimes companies do fail. That’s just the way it is in our system,” said White House press secretary Dana Perino.

Mrs. Pelosi and Senate Majority Leader Harry Reid, Nevada Democrat, say they are prepared to call Congress back to another lame-duck session next week if the automakers can make a persuasive case for aid.

Backed by a major lobbying blitz from major business and labor groups, executives from the Big Three were on Capitol Hill on Wednesday giving closed-door briefings to members and key staffers ahead of the next two days of hearings.

One option being explored is to provide the companies with a smaller “bridge loan” to keep them solvent until Mr. Obama takes office Jan. 20. But how much money would be enough and which fund would be used to finance the bailout are still uncertain.

There is also talk of an expedited bankruptcy filing, with the government providing the funds to keep the automakers’ operations running smoothly while they resolve funding, credit and cost problems.

The automakers maintain that they have been blindsided by a global credit crunch and recession that has caused sales to plummet. Skeptics counter that the industry’s wounds are largely self-inflicted, the product of years of bad design, engineering, marketing and financial decisions.

Andrea Billups reported from Detroit; David R. Sands from Washington. S.A. Miller and Jon Ward contributed to this report from Washington. Christina Bellantoni contributed from Chicago.