The stalemated debate over the federal payroll tax holiday wore on Monday as Senate Democrats announced a slimmed-down proposal that would push rates even lower for millions of Americans next year. Meanwhile, President Obama used his White House megaphone to urge Congress not to leave town for the holidays without at least extending tax cuts that are set to expire at the end of the year.

But the Democrats’ latest proposal, worth $185 billion, would still be paid for in part by a new surtax on those making more than $1 million a year, the same plan that doomed earlier efforts.

The new levy led Republicans to block a $265 billion payroll-tax-cut bill in the Senate last week and is likely to lead to continued opposition when the new version is put to a vote, probably this week. Republicans said Monday that they continue to oppose cutting one tax by raising another on those they think are best positioned to spark job growth.

Democrats portrayed the new proposal as a form of compromise because the bill carries a smaller price tag and would be paid for in part with GOP proposals to ensure that wealthy Americans don’t receive unemployment benefits or food stamps.

“This is a serious proposal, and Republicans should take it seriously,” said Senate Majority Leader Harry M. Reid (Nev.).

Monday’s maneuvering took place as Congress races to find a compromise that would extend a one-year reduction in the payroll tax rate from 6.2 percent to 4.2 percent

Without an agreement by New Year’s Eve, taxes will increase by $1,000 next year for the average family.

Leaders in both parties have said they think the tax break should be extended, allowing consumers to spend more of their pay and help the ailing economy.

But the two sides have been arguing over how to continue the tax break without increasing the federal deficit or undermining the solvency of Social Security, which is funded through the 12.4 percent payroll tax that is split between workers and their employers.

The issue is proving particularly tricky for Republican leaders, who are not eager to hand Obama a victory but understand the political peril if their usually tax-averse party were to unify in opposition to a tax break that benefits middle-class workers.

And, as they have repeatedly had to do since taking control of the House this year, GOP leaders must contend with a revolt from rank-and-file members, many of whom would prefer a comprehensive rewrite of the tax code that would permanently lower rates rather than a temporary break on one tax.

House Republicans are working on their own alternative, hoping to overcome objections from many of their members who have resisted extending the tax holiday, arguing that it would not spur hiring.

But a majority of Republicans joined Democrats last week in blocking a similar GOP-sponsored proposal in the Senate that would have extended the tax cut but paid for it by imposing a three-year pay freeze for federal workers and shrinking the federal workforce.

At the White House on Monday, Obama urged congressional Republicans to join Democrats in approving the extension.

“How could it be that the only time there’s a catch is when it comes to raising taxes on middle-class families?”he said in the White House briefing room. “How can you fight tooth and nail to protect high-end tax breaks for the wealthiest Americans and yet barely lift a finger to prevent taxes going up for 160 million Americans who really need the help? It doesn’t make sense.”

The president has made extending and expanding the tax holiday the centerpiece of his $447 billion jobs plan, proposing that employees pay only 3.1 percent in payroll tax next year — resulting in a $1,500 tax break for the average family. He also suggested that some expanding businesses should receive a 2 percent cut in their payroll taxes.

Only one Republican — Sen. Susan Collins (Maine) — voted with Democrats on a Senate bill last week that mirrored Obama’s proposal and would pay for it with a new 3.25 percent tax on annual income over $1 million.

The latest Senate version, offered by Sen. Robert P. Casey Jr. (D-Pa.) would no longer provide a tax cut to employers. It would pare down the surtax on income over $1 million from 3.25 percent to 1.9 percent and make the surtax temporary, expiring after 10 years.

It also would adopt deficit-reducing measures from the recent deficit-reduction negotiations, Casey said, raising $38.1 billion by increasing fees that Fannie Mae and Freddie Mac charge mortgage lenders.

But the inclusion of the tax on millionaires probably will kill any chance of passage, and is considered a sign that Democrats are pressing their political advantage by forcing another difficult vote on Republicans.

Ultimately, both sides have said they think a negotiated compromise between Democrats and Republicans in the House and the Senate will be necessary to find a tax holiday solution that is acceptable to both parties.

“If the president wants to make progress, he should insist that Senate Democrats remove the job-killing small-business tax hike from their partisan proposal,” said Michael Steel, a spokesman for House Speaker John A. Boehner (R-Ohio).

Boehner has floated the idea of attaching to the payroll extension other conservative proposals, such as a bill that would mandate a speedy decision from the State Department on a proposed energy pipeline from Canada to the Gulf Coast.

Staff writers William Branigin and Felicia Sonmez contributed to this report.