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The bankruptcy, to be filed in New York, is a moment of reckoning for an industry that was once at the heart of the American economy. It culminates a remarkable four months of confrontation between Washington and Detroit that is expected to result in a drastic downsizing of the company.

It also places the government in uncharted territory as a business owner, as it takes a 60 percent ownership stake in the company during its restructuring.

Reflecting the government’s extraordinary intervention in industry, aides say, Mr. Obama plans to tell the nation on Monday that he believes G.M. can be brought back from the brink of insolvency, even if the company looks almost nothing like the titan of old.

Meanwhile, a federal judge late Sunday night cleared a path for Chrysler to get out of bankruptcy by approving a sale of most of that carmaker’s assets to a new entity to be run by Fiat of Italy.

Administration officials briefed reporters on the G.M. plans Sunday night, as President Obama began to inform members of Congress. But the White House insisted that the aides who talked to reporters could not be named.

In his remarks on Monday, Mr. Obama will spell out a strategy in which a shrunken G.M. can make money even if new car sales remain at a sluggish 10 million a year in the United States and even if G.M., once the giant of the industry, drops below its current 20 percent market share in this country.

But to get there, American taxpayers will invest an additional $30 billion in the company, atop $20 billion already spent just to keep it solvent as the company bled cash as quickly as Washington could inject it. Whether that investment will ever be recovered is still an open question.

The company will also have to shed 21,000 union workers and close 12 to 20 factories, steps that most analysts thought could never be pushed through by a Democratic president allied with organized labor.

Forty percent of the company’s 6,000 dealers will close, the workers’ union will be forced to finance half of its $20 billion health care fund with stock of uncertain value in the restructured G.M., and bondholders, including many retirees, will be forced to take stock worth 10 cents for every dollar they lent the company.