And Democrats are no more eager than Republicans, with control of both houses of Congress up for grabs, to vote for the large revenue increases that a grand bargain would entail. They do not want to limit popular but costly deductions, as Mr. Obama and past bipartisan panels, like his Simpson-Bowles fiscal commission, have proposed. That is especially true for Democrats from states, like California and New York, where affluent voters value deductions for mortgages on first and second homes, charitable giving, and state and local taxes.

“It’s a lot harder than you’d think to find Republicans who’d actually want to cut entitlements, or Democrats who want to raise taxes,” said Jared Bernstein, a former economic adviser to Vice President Joseph R. Biden Jr. and now a senior fellow at the liberal Center on Budget and Policy Priorities. “The only person who seems to have consistently been interested in a grand bargain is the president, and frankly I’m not even sure about him.”

Mr. Obama has not pressed the negotiators from the Democratic-controlled Senate and the Republican-led House to aim higher. It would not matter if he did, lawmakers say, particularly given his diminished political standing after weeks of controversies over his Affordable Care Act.

But even a stronger president would be virtually powerless to engineer a multiyear grand bargain now. Negotiators are struggling just to keep alive their talks for a minimalist compromise, one that would replace the arbitrary across-the-board cuts known as sequestration for the next year or two.

In his budget this year, Mr. Obama outlined specific long-term trade-offs on taxes and the entitlement programs — chiefly Medicare, Medicaid and Social Security — to save about $1.8 trillion over a decade. The savings would come on top of the roughly $2 trillion in 10-year spending cuts and tax increases that both sides have agreed to since 2011. Taken together, the deficit reduction package proposed by Mr. Obama is roughly in line with the Simpson-Bowles recommendations for a 10-year mix of tax increases, reduced spending on entitlement programs, and cuts in military and domestic programs that are budgeted annually.