“G.M. is the biggest of the three and it’s in the worst shape,” said John Casesa, principal in the auto consulting firm Casesa Shapiro Group. “I think it would be a pretty big blow to Rick if they don’t get the money.”

The debate on Capitol Hill will focus on whether the Detroit automakers can get $25 billion in aid immediately from either the Treasury Department’s $700 billion financial rescue program, or from an existing loan program aimed at improving the fuel-efficiency of Big Three vehicles.

Ford and Chrysler, however, have not made the same dire predictions about their businesses  putting the urgency of the bailout squarely on the shoulders of Mr. Wagoner and G.M.

Some members of Congress have suggested that a management change is necessary at G.M. before any loans can be made.

“I do not support the use of U.S. taxpayer dollars to reward the mismanagement of Detroit-based auto manufacturers,” said Senator Richard Shelby, the ranking Republican on the Senate Banking Committee, which holds its hearing on the bailout on Tuesday afternoon.

The lanky, 6-foot-4-inch Mr. Wagoner, a 55-year-old former Duke University basketball player and Harvard Business School graduate, has refused to consider resigning even if it would help G.M.’s chances of getting emergency aid.

Image Rick Wagoner, G.M.'s chief for the last eight years, has to convince Congress that the automakers need federal loans. Credit... Bill Pugliano/Getty Images

G.M. has declined to make Mr. Wagoner available for interviews. In a Nov. 10 interview with the trade journal Automotive News, however, he said that a change in management at G.M. would not be wise at such a crucial time for the company. “I don’t think it’d be a very smart move,” he said. “I think our job is to make sure we have the best management team to run G.M. It’s not clear to me what purpose would be served.”