(Reuters) - President Barack Obama demanded Tuesday that House Republicans pass a short-term extension of a payroll tax cut, showing an unwillingness to back down in a fight that could result in higher taxes for 160 million Americans.

The Republican-led House earlier rejected a short-term deal passed by Democrats and fellow Republicans in the Senate over the weekend and called for fresh negotiations on the expiring tax break that saves the average American worker $1,000 a year.

As both sides dug more deeply into entrenched positions, House Speaker John Boehner, the top Republican in Congress, demanded Obama order Senate Democrats back into session to haggle over a year-long extension.

I need the president to help out, Boehner told reporters, drawing applause from a large group of Republican lawmakers standing behind him in the Capitol.

The show of solidarity stood in contrast to the revolt by conservative and Tea Party-backed House Republicans after Boehner was reported to have initially sought their support for the shorter extension over the weekend.

Boehner has struggled to control his restive caucus all year, with many members refusing to negotiate with Democrats, pushing the federal government to the brink of three shutdowns and the edge of a debt default.

In a surprise appearance in the White House briefing room, a visibly frustrated Obama told lawmakers to put politics aside. Let's not play brinkmanship, he said.

The clock is ticking. Time is running out. And if the House Republicans refuse to vote for the Senate bill or even allow it to come up for a vote, taxes will go up in 11 days, he said.

Some House members were already departing Washington to head home for the holidays on Tuesday evening, joining their Senate counterparts who left earlier in the week.

Prospects for the Democratic-controlled Senate reopening negotiations remained dim as Senate Majority Leader Harry Reid insisted he would not reconvene the chamber. Reid has won backing from some Republicans in the Senate, who have called on their colleagues in the House to back the deal.

Reid will stick to his guns and refuse to reopen negotiations, a senior Democratic aide said after the House vote. Taxes will go up - or Boehner will cave, the aide said.

Both parties believe they have the upper hand in the year-end battle. Republicans are betting Democrats fear a voter backlash in 2012 if the tax break expires and will eventually bow to their demands. Democrats, however, are gambling the same is true for Republicans.

The House Republican demand for a one-year extension marks a surprising turnabout since for months they were openly skeptical of its economic benefits. Now they argue a two-month extension creates uncertainty for workers and employers and is unworkable.

RECESSION THREAT

The Senate passed the short-term extension on Saturday because Republicans and Democrats could not agree on how to pay for it for a full year. It was not clear how House Republicans hope to overcome that hurdle.

The U.S. Treasury Department weighed into the debate for the first time, saying while it would prefer a full-year extension, it could ensure smooth implementation of the short-term measure for employers.

Failure to extend the tax break and benefits for millions of unemployed Americans, which expire on Dec. 31, could heighten the possibility of a U.S. recession in 2012, some economists have warned.

You're either going to have an OK rate of economic growth next year or a pretty subpar one, and it will be determined in large part by U.S. politicians, said Eric Lascelles, chief economist at RBC Global Asset Management in Toronto.

Unless signs of compromise emerge, the most likely scenario would be a January 1 snap-back in the payroll tax rate to 6.2 percent of wages from 4.2 percent, reducing take home pay as holiday bills come due.

As the odds of a missed deadline rise, several economists said the economy could survive nearly unscathed if there is a short delay in extending the tax break.

If it is a week or two, it is annoying but the impact would be fairly small, said Nigel Gault, U.S. economist at economic forecasting firm Global Insight.

If the tax hike happens, Congress could return in early January to reach a deal that could result in a retroactive reduction, or refund of any higher taxes collected.

But there is still time for negotiations through the end of next week, and Obama, who has delayed his vacation to Hawaii, could take a more active role.

Many had expected the year-end negotiations on renewing the tax break would be difficult, but what had been thought to be a brawl has exploded into a full-scale battle.

Washington gridlock and dysfunction is fueling an anti-incumbent mood among voters heading into next year's elections, with Congress' popularity at a very low 11 percent. The political bickering also has led to rating agency Standard & Poor's cutting America's prized AAA credit rating.

The biggest sticking point for a year-long extension is how to cover the $120 billion in lost revenue to the Social Security Trust Fund. Republicans are demanding spending cuts to cover the cost and Democrats want to pay for it by closing some tax breaks for the wealthy.

The Senate bill included a provision demanded by House Republicans that would force Obama to accelerate a decision on TransCanada Corp's Keystone XL oil pipeline project between Canada and Texas, which is backed by some labor unions but opposed by environmental groups.

(Additional reporting by Paul Eckert, Donna Smith, Leah Schnurr, Rachelle Younglai, Kim Dixon and Caren Bohan; Writing by David Lawder and Deborah Charles; Editing by Ross Colvin and Eric Walsh)