The proposal by Mr. Romney, the Republican presidential nominee, was envisioned to help pay for an across-the-board income tax cut, a move ridiculed by President Obama as window dressing to a "sketchy deal." But many Democrats now see it as an important element of a potential deficit reduction agreement — and one they can claim to be bipartisan.

The cap — never fully detailed by Mr. Romney — is similar to a longstanding proposal by Mr. Obama to limit income tax deductions to 28 percent, even for affluent households that pay a 35 percent rate. But a firm cap of around $35,000 would hit the affluent even harder than Mr. Obama's proposal, which has previously gotten nowhere in Congress.

"Let's just say there's a renewed interest," said Senator Kent Conrad, Democrat of North Dakota and chairman of the Senate Budget Committee. "Part of it is people reflecting on Obama's proposal, but when Romney said what he said, it just added fuel."

"I was a little surprised Romney proposed a dollar cap when he did it," Mr. Conrad added.

The attention on the plan is evidence that ideas on deficit reduction are beginning to take firmer form as the January deadline for dealing with expiring tax cuts and automatic spending reductions draws close. The lame-duck session that begins Tuesday could be one of the most pivotal in years, and the political atmosphere is considerably different than when lawmakers left in October for the fall campaigns.

President Obama has been re-elected convincingly. Democrats, once in danger of losing control of the Senate, instead gained at least one seat. House Republicans held control, but as many as 16 incumbents lost, including some of the party's most uncompromising voices, like Representatives Joe Walsh of Illinois and Allen B. West of Florida, who refuses to concede his seat despite his continuing deficit in the vote count. The somber mood among Republicans could ease negotiations to avert more than $500 billion in automatic spending cuts and tax increases.

"The worst time to work together on a bipartisan basis is right before an election," said Representative Jeb Hensarling of Texas, chairman of the House Republican Conference. "The best time to work on a bipartisan basis is right after an election."

Returning lawmakers will find a long to-do list greeting them Tuesday and seven short weeks to do it. In the House, members may once again try to grapple with the farm bill, which expired during the recess. Dairy farmers in particular are clamoring for a resolution, and a year of record drought gave urgency to a bill.

Across the Rotunda, the Senate may once again take up a cybersecurity bill. An earlier measure that would have established optional standards for the computer systems that oversee the country's critical infrastructure was stopped by a filibuster as some leading Republicans yielded to the concerns of major business interests; members from both parties would like to see a renewed effort on a bill as soon as possible. A military policy bill, which generally passes easily on the floor, was caught up in the fight over looming Pentagon cuts and did not make it to the floor.

But the most pressing task is averting the sudden expiration of all the Bush-era tax cuts, a payroll tax cut and unemployment benefits at the same time that across-the-board military and domestic spending cuts kick in. Most economists believe that "fiscal cliff," if not mitigated, would send the economy back into recession. Democrats say any plan to avert the crisis must include a combination of tax increases on the rich and spending cuts. Republicans say they are willing to overhaul the tax code to increase federal revenue, but they refuse to raise income tax rates.

That has kicked off a scramble to find ways to raise revenue without higher rates by closing loopholes and tightening deductions and tax credits. Senior Democrats made clear Monday that the search for such tax changes should not be seen as a replacement for higher tax rates on the rich.

Representative Chris Van Hollen of Maryland, the top Democrat on the House Budget Committee, said the Romney proposal to cap deductions would work only in concert with allowing the top two income tax rates to revert to the level of Bill Clinton's presidency, 36 percent and 39.6 percent, up from the current 33 percent and 35 percent.

To come close to the level of deficit reduction needed to get the nation's fiscal house in order, the presidential deficit reduction commission known by the names of its chairmen, Erskine B. Bowles and Alan K. Simpson, assumed those top rates would jump, Mr. Van Hollen said. But beyond those rate increases, more revenue will have to be raised.

"This is a promising idea for tax reform," Mr. Van Hollen said, "if you start at the higher Clinton era rates for high-income earners."

The idea gained currency when Martin Feldstein, a prominent Republican economist and former chairman of Ronald Reagan's Council of Economic Advisers, embraced it during the campaign to show that Mr. Romney's tax plan was not as far-fetched as Democrats portrayed it. Maya MacGuineas, president of the Committee for a Responsible Federal Budget and something of a ringleader in the search for a bipartisan deficit deal, has also embraced the idea.

But with the presidential campaign over, it is taking on new salience. The Democratic centrist group Third Way has made it the centerpiece of a package of tax changes that it says could raise nearly $1.3 trillion over 10 years without raising rates.

The Third Way proposal would limit tax deductions to $35,000 but would exclude charitable giving. Universities, foundations and other philanthropies have been the biggest impediment to passing Mr. Obama's more modest 28 percent limit, which did not exclude the charitable tax deduction.

Jennifer Steinhauer contributed reporting.