WASHINGTON — Humbled and increasingly desperate as car sales plummet, the heads of Detroit’s Big Three automakers said Thursday they were willing to accept government oversight of their spending in return for $34 billion in government loans to keep them afloat.The chief executives said they would be willing to take the money in stages, which would allow the government to put the brakes on additional funding if the companies were not making solid progress in reinventing themselves as leaner, more profitable enterprises.But skepticism remained high on Capitol Hill, with lawmakers questioning the automakers’ commitment to becoming more competitive and worrying that taxpayers’ money would be quickly frittered away. As a result, General Motors, Ford and Chrysler still faced tough odds in getting government help this year.“In just two short weeks, the price tag has jumped” from $25 billion to $34 billion, said Sen. Richard Shelby, R-Ala., the Senate Banking Committee’s top Republican. “I’m interested in hearing what changed and why we should believe things will get better.”Democrats generally are more sympathetic to the automakers’ plight, saying thousands of jobs could be lost and the nation’s industrial sector might be put in jeopardy.“None of us relishes this task that we are asked to consider, yet who among us believes we should risk the consequences of the collapse of . . . one or more domestic automobile manufacturers?” Banking Committee Chairman Chris Dodd, D-Conn., said at the start of a nearly six-hour hearing. “Make no mistake about it — those consequences would be severe and sweeping.”The auto executives face another grilling today when they appear before the House Financial Services Committee.The idea of paying out government funds in pieces instead of all at once appeared to gain traction among members of Congress, although nothing approaching a final deal was at hand.As described to the auto executives who accepted it, the proposal calls for about half the money to be disbursed quickly to keep the companies afloat through March 31. The rest would be held until a government board of trustees was convinced the companies were making progress toward becoming more competitive and retooling their lineups to offer more fuel-efficient cars.Sen. Chuck Schumer, D-N.Y., pushed the idea of a single trustee designated by the president to control disbursement of additional money after March 31 and to force changes on the companies and the United Auto Workers union, which has been criticized for protecting current compensation packages for its members."I think that there’s a general view that we want to see the conditions before we give you the money. And you folks sort of want the money and then say, ‘Let the conditions work out,’ " Schumer said. “I don’t trust the car companies’ leadership. . . . I worry that, if they’re left on their own, they’ll be back a short time later asking for more, and we won’t be better off.”The company executives said they welcomed the prospect of government oversight."It would be very helpful for us, whether it’s a board or an individual, to have someone to work with on this, to submit our proposals, and then for that person to say, ‘OK, don’t agree with that. You’ve got to change this,’ " GM Chief Executive Rick Wagoner said.Another idea floated at the hearing was to force banks that have received bailout money to lend to the automakers, with government guarantees on the loans. That would require federal officials to renegotiate the terms of the capital injections.Some suggested that Chrysler and GM should be required to merge.In their appearance before the Banking Committee, the attitude of the company executives was markedly different from what it was in November, when they first argued for a bailout.In the earlier hearing, they were vague, evasive and mostly unwilling to agree to requests by lawmakers for concessions in exchange for emergency loans. On Thursday, the executives were so eager to please that they agreed to almost every request from committee members.For example, in the earlier appearance before Congress, only Chrysler Chief Executive Officer Bob Nardelli agreed to reduce his annual salary to $1. Now, all three have agreed.Also, faced with sharp criticism for traveling to Washington for those hearings in separate private jets, the CEOs all drove from Michigan in advanced hybrid cars this time.“It used to be that our goal was simply to compete. Now we are absolutely committed to exceeding our customers’ expectations for quality, fuel efficiency, safety and affordability,” Ford Chief Executive Officer Alan Mulally told the committee. “In short, we are on the right path to becoming a profitable, growing company.”Dodd and several other senators declared themselves largely satisfied with the plans and said they were searching for a way to pass a bailout soon.“Nothing concentrates the mind like a death sentence,” Dodd said.