Back-to-back voice vote approvals of the measure by the Senate and House capped a retreat by House Republicans who had insisted that a full-year bill was the only way to prevent an immediate tax increase on Jan. 1.

The measure passed despite lingering grumbling from tea party Republicans. It buys time for negotiations early next year on how to finance a year-long extension of the 2 percentage point Social Security payroll tax cut.

It will keep in place a salary boost of about $20 a week for an average worker making $50,000 a year and prevent almost 2 million unemployed people from losing jobless benefits averaging $300 a week.

Passage in the House — Friday’s action on the measure took less than a minute — capped a swift retreat by House Republicans. Their move to force a holiday season confrontation with Obama and Senate Democrats had threatened to hit 160 million workers with a tax increase on Jan. 1. But it backfired badly.

Just 24 hours earlier, House leaders had insisted the only way to prevent that tax hike and a phase-out of jobless benefits for people out of work for more than six months was to pass a full-year renewal.

Those goals had been embraced by virtually every lawmaker in the House and Senate but had been derailed in a quarrel over demands by House Republicans for immediate negotiations on a long-term extension bill. Senate leaders of both parties had tried to barter such an agreement among themselves a week ago but failed, instead agreeing upon a 60-day measure to buy time for talks next year.

Thursday’s decision by House Speaker John Boehner, R-Ohio, to cave in to the Senate came after days of criticism from Obama and Democrats. But perhaps more tellingly, GOP stalwarts including strategist Karl Rove and the Wall Street Journal editorial board warned that if the tax cuts were allowed to expire, Republicans would take a political beating that would harm efforts to unseat Obama next year.

House GOP arguments about the legislative process and what the “uncertainty” of a two-month extension would mean for businesses were unpersuasive, and Obama took the offensive.

Friday’s House and Senate sessions were remarkable. Both chambers had essentially recessed for the holidays but leaders in both parties orchestrated passage of the short-term agreement under debate rules that would allow any individual member of Congress to derail the pact, at least for a time. None did.

The developments were a clear win for Obama. The payroll tax cut was the centerpiece of his three-month, campaign-style drive for jobs legislation that seems to have contributed to an uptick in his poll numbers — and taken a toll on those of congressional Republicans.