WASHINGTON — With both parties positioning for difficult negotiations to avert a fiscal crisis as Congress returns for its lame-duck session, Democrats are latching on to an idea floated by Mitt Romney to raise taxes on the rich through a hard cap on income tax deductions.

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.”