WASHINGTON — The House is gone, mostly. The Senate vows not to return. And President Obama is home 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 in Washington after a year of acrimony and stalemate came to a head on Capitol Hill, leaving millions of American workers facing a tax hike in two weeks that would cost the typical family $1,000 a year.

The House voted Tuesday to reject a Senate compromise that would have extended a federal payroll tax break 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.

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 imposing higher taxes on the wealthy.

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

“It’s like deja vu all over again. It’s like (the movie) ‘Groundhog Day,’ ” said Rep. Henry 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 89-10 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 Social Security payroll tax break in place next year, rather than allowing the tax rate to jump from 4.2 percent to 6.2 percent. On Tuesday, the White House said he would remain in Washington to get the issue settled. It would not say whether he still plans to join his family in Hawaii for the holiday at some point. But he did not seem 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.

“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 voted 229-193, with no Democratic support, 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 work out a deal.

“We’ve done our work for the American people,” said House Speaker John 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 that 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 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 Friday believing that Boehner and his top deputy, House Majority Leader Eric Cantor of Virginia, 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.

But McConnell, a 27-year veteran 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 lined up 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.

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 fees charged by Fannie Mae and Freddie Mac on lenders to guarantee loans. That’s the money the Senate used for its smaller, $33 billion two-month deal.

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

As the last vote was called in the House on Tuesday – on a resolution restating House support for its own payroll tax bill adopted last year – 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.