Asked if Republicans might filibuster the president’s backup plan, Senator John Barrasso of Wyoming, a member of the Republican leadership, said on “Fox News Sunday”: “I just don’t think this is going to solve the problems — it actually doesn’t solve the problems. We have a spending problem in this country.”

Besides, Mr. Stewart said, Democrats have yet to detail the legislation they want a vote on. The Senate passed legislation in July to extend expiring income tax rates on income under $250,000, but divided Democrats could not agree on a new level for the estate tax, which is also scheduled to rise in January, nor did they include a provision to stave off $100 billion in across-the-board cuts to defense and domestic programs next year.

Mr. Obama, speaking to reporters Friday, left critical details out of his description of the plan he wants Congress to pass. Although he favors allowing the estate tax rate of 35 percent on inheritances over $5 million to rise to 45 percent on estate values over $3.5 million, for example, he did not say how such taxes should be treated as part of his stopgap fiscal plan. If nothing is done, the estate tax will jump to the Clinton-era level, 55 percent, on estate values over $1 million.

Nor did the president say what he wanted to do about expired business tax provisions, like the research and development tax credit, which is scheduled to disappear on Jan. 1. He gave no instructions about a long-delayed law that, absent Congressional action this week, would sharply cut reimbursements for physicians treating Medicare patients, starting next month.

“What is it, exactly, that we’re supposed to respond to or work with?” Mr. Stewart said. Referring to the Senate majority leader, Harry Reid of Nevada, Mr. Stewart continued: “Reid is the majority leader. Maybe for once he could propose something that he actually thinks could pass.”

The impending cuts were set in motion last year when the Budget Control Act ended an impasse over raising the nation’s borrowing limit with a deal designed to hurt both parties if they did not strike an agreement later on. A committee came up with at least $1.2 trillion in cuts over 10 years that would come automatically, half to national security and half to domestic programs.

The measure that Mr. Obama and Democratic leaders are considering would contain all the provisions of a tax bill that the Senate passed in July, according to a Democrat familiar with the discussions. That bill included an adjustment to the alternative minimum tax — a parallel income tax that is designed to make sure the affluent do not escape taxation but that is increasingly hitting the middle class — as well as several tax credits for middle- and low-income workers that are also due to expire.