The House is gone, mostly. The Senate vows not to return. And President Obama is home in Washington while his family vacations in Hawaii, hoping for some kind of agreement between the two that he can sign.

That was the uneasy state of play Tuesday after a year of acrimony and stalemate came to a head on Capitol Hill, leaving millions of American workers facing a tax increase in two weeks.

The House voted on Tuesday to reject a Senate compromise that would have extended a federal payroll tax holiday for two months, continued unemployment benefits for the long-term jobless and averted a cut in the reimbursement rate for doctors who treat Medicare patients.

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At its heart, the fight over the tax cut is only the latest incarnation of the same ideological clash that has afflicted Congress for the past year, over what the government should fund and how it should be paid for.

Once again, Democrats and Republicans foundered over whether to fund an initiative by cutting entitlements and other spending or by raising taxes on the wealthy.

It’s the same argument that foiled the “supercommittee” on deficit-reduction this fall and fed the summer’s contentious debate over raising the federal debt ceiling.

“It’s like deja vu all over again. It’s like ‘Groundhog Day,’ ” said Rep. Henry A. Waxman (D-Calif.).

After Tuesday’s vote, Democrats held to their position that the Senate deal already represented a bipartisan compromise — crafted by the chamber’s two top leaders and adopted on an 89-to-10 vote — and that there was no reason for the Senate to reopen negotiations.

Following a pattern that developed as they lurched from one crisis to another all year, each side appeared to believe that the pressure of an impending deadline and angry public reaction would force the other to capitulate.

Obama has been lobbying for months to keep the expiring tax cut in place next year, rather than allowing the tax rate on wages to jump from 4.2 to 6.2 percent and on Tuesday the White House said he would remain in Washington to get the issue settled — but would not say whether he still plans to join his family in Hawaii for the holiday at some point. But he did not seem to be in the mood to negotiate.

White House advisers believe Obama has gained political ground during the weeks of fighting with Republicans over his jobs package and the payroll tax cut.

The president has tried to position himself as a champion of the middle class, and two new polls this week show his approval ratings rising to the upper 40s, their highest level since the summer. Conversely, the public’s opinion of Congress has continued to fall.

Late Tuesday, the White House launched a new public pressure campaign around the issue — asking people to weigh in on Twitter and Facebook about what $40, the average savings per paycheck provided by the tax cut, means to them.

“Let’s be clear: Right now the bipartisan compromise reached on Saturday is the only viable way to prevent a tax hike on January 1,” Obama said not long after the House vote. “Do not play brinksmanship. The American people are weary of it, tired of it. They expect better.”

House Republicans rejected the deal 229 to 193, with no Democratic votes, to set aside the Senate deal. GOP critics argued that the two-month deal would inject new uncertainty into a still-sluggish economy. They said they were prepared to work through the holidays to reach a deal.

“We’ve done our work for the American people,” said House Speaker John A. Boehner (R-Ohio). “Now it’s up to the president and Democrats in the Senate to do their work as well.”

To prove the point, eight members appointed by GOP leaders as designated negotiators might gather on their own in coming days. But, with floor action complete, many other House members left Washington to celebrate Christmas, available to return on 24 hours’ notice if needed.

The undoing of what many on both sides of the aisle thought was a deal on Saturday is a reflection of the continued difficulty Boehner has had in managing his cantankerous caucus.

Repeatedly, over the past year, he has allowed some of the most conservative members, particularly an influential group of freshmen, to call the shots at crucial moments.

This time, Boehner and his leadership team may have allowed the House Republicans to place their party in real political peril with no obvious exit strategy.

Senate Minority Leader Mitch McConnell (R-Ky.) left a meeting with House leaders on Friday believing that Boehner and his top deputy, House Majority Leader Eric Cantor (Va.), would find the votes to approve a two-month extension of the tax holiday. Both Boehner and Cantor have since disavowed giving McConnell the go-ahead to make the deal, and McConnell has issued a statement supporting Boehner’s position.

Regardless of what exactly was said, McConnell, a 27-year member of the Senate, has a reputation as a master negotiator, known for playing hardball and then cutting the best deal possible; he has no history of communication errors.

McConnell allied 39 of the GOP’s 47 votes in the Senate to pass the measure, allowing the chamber to triumphantly close for legislative business this year.

Then came the House rebellion.

McConnell has not been seen in public since Saturday’s vote, and a growing number of Senate Republicans have urged Boehner to cave, while rank-and-file House Republicans have called their Senate counterparts “lazy” for accepting the deal and demand that the extension be for an entire year.

A package that would extend the tax cut for the full year, as well as unemployment benefits and Medicare rates, would cost about $200 billion.

The two sides have been wrangling for weeks over how to replenish Social Security, which is funded by payroll taxes. They’ve agreed to cover $36 billion of the cost by raising the fees Fannie Mae and Freddie Mac charge lenders for guaranteeing loans. That’s the money the Senate used for its $33 billion two-month deal.

But they have not been able to close the gap on a full-year deal.

In the bill the House passed last week, Republicans suggested entitlement cuts — proposing an increase in Medicare premiums for upper-income seniors — as well as freezing federal salaries and shrinking the federal workforce.

Democrats instead have sought to raise taxes on the wealthy to offset the payroll tax cut, which is enjoyed by middle-income workers. Under Obama’s American Jobs Act — which would have cut the payroll tax rate to 3.1 percent and expanded it to more employers — the tax cut would be paid for by limiting tax deductions for families making more than $250,000 a year. Senate Democrats instead proposed a surtax on those making more than $1 million a year.

House Republicans insisted Tuesday that the two sides were not far apart and that further talks could bridge the differences.

“We want to sit down, and find out where we can resolve the differences, and they’re narrow,” Cantor said on MSNBC’s “Andrea Mitchell Reports.”

Obama said Senate leaders “made good progress” in talks last week but decided that more time was needed to resolve the dispute and called for the two-month deal to be passed as “an insurance policy” against a tax increase.

That deal included a provision that would have required the Obama administration to make a speedy decision on the controversial Keystone XL oil pipeline, a concession to House Republicans who don’t believe the tax cut is a good way to stimulate the economy.

Many Democrats charged Tuesday that continued GOP reluctance to extend the payroll tax cut was the true cause for the Republican opposition.

As the last vote was called in the House on Wednesday — a resolution restating House support for its own payroll tax bill adopted last week — lawmakers left clearly believing their work was done through Christmas.

“All right! Woo-hoo!” said Rep. Marsha Blackburn (R-Tenn.), her coat under her arm, heading for the Capitol doors.

Staff writers Felicia Sonmez and David Nakamura contributed to this report.