The ice cracked under House Speaker John Boehner on Thursday. A deal to quiet a bruising political eruption over the payroll tax finally took shape -- after relentless criticism from within GOP ranks that House Republicans had dug themselves knee-deep in quicksand.

After days of thrashing and teeth-gnashing, Republican Senate Minority Leader Mitch McConnell offered a way out of the mess with a statement underscoring similarities between the measures in the two chambers, rather than differences.

The House reversed course after a contentious 5 p.m. phone call among Boehner and his caucus, during which members agreed to approve a slightly tweaked Senate-passed measure to extend the payroll tax for two months into 2012. In exchange, Senate Democrats and President Obama agreed to negotiate with House Republicans a longer-term payroll tax extension that could help buoy the economy next year when that short-term extension expires.

The agreement also extends unemployment insurance for two months and keeps in place existing Medicare reimbursement rates for doctors.

“Senator Reid and I have reached an agreement that will ensure taxes do not increase for working families on January 1 while ensuring that a complex new reporting burden is not unintentionally imposed on small business job creators,” Boehner said in a written statement late Thursday that he subsequently read at a news conference.

The speaker said House and Senate lawmakers will be asked to approve the deal by unanimous consent “before Christmas.” That action will come Friday. Seeking unanimous consent -- a risky approach, since a single House member could object and thwart Boehner’s efforts to move beyond the infighting -- carries the benefit of speed, and also prevents reluctant GOP members from having to put their names next to a floor vote they may have opposed.

When asked by a reporter if he was certain he had support from his members to conclude the deal on Friday, Boehner said, “I don’t know. . . . It’s not always easy to do the right thing. . . . We fought the good fight.” If the effort to capture unanimous consent from his caucus fails, Boehner said he would return next week to seek a roll-call vote on the two-month extension.

“I think this agreement will help our economy,” he said in the Capitol. “We were able to fix what came out of the Senate,” he added.

Boehner’s leadership has been tested throughout 2011 by some of the most conservative firebrands in his conference. The payroll tax drama is the latest in a series of crises that have stirred speculation that Boehner’s hold on the speakership is in jeopardy.

Obama, on the other hand, came out of the drama stronger than when he went in. The president immediately issued a written statement congratulating lawmakers for “ending the partisan stalemate.” Calling the agreement “good news just in time for the holiday,” he added, “This is the right thing to do to strengthen our families, grow our economy, and create new jobs. This is real money that will make a real difference in people’s lives.”

On Friday, the president is expected to sign a $1 trillion omnibus spending bill to keep the government operating, and several other measures. He may fly to Hawaii to join his family for Christmas either Friday or Saturday.

Obama first proposed an extension of the payroll break, plus an even more generous version that lawmakers rejected this fall, when he unveiled his American Jobs Act in September.

During a White House event early Thursday, the president had predicted a deal was all but assured. “I believe it's going to happen sooner or later,” he said while surrounded by 16 local taxpayers who had written to the White House in support of the tax break. “Why not make it sooner, rather than later?” he asked.

The timing and the details of a compromise had been question marks since Saturday. That’s when the Senate, initially believing it had brokered a bipartisan deal to keep payroll taxes from rising on Jan. 1, voted 89-10 to continue the 2 percent, temporary reduction for at least eight weeks in 2012. Obama agreed to that compromise, which included numerous administration concessions, but before the president was pressed to explain the weak victory he had achieved, conservative House Republicans, many of them freshmen, balked at the compromise and turned the debate into a GOP free-for-all.

Obama and Senate Democrats -- barely able to believe their good fortune -- had been hanging back for five days as House and Senate Republicans battled one another, hurtling headlong toward an effective tax hike for 160 million Americans just a week after Christmas.

On Thursday morning, McConnell issued a written statement suggesting how House Republicans and Senate Democrats were close enough to an agreement to work out a compromise that would prevent taxes from going up on Jan. 1, and preserve a forced expedited review by the administration of a controversial oil pipeline project attached to the payroll package. Obama originally opposed that provision, but swallowed it last Saturday. The minority leader’s move was vintage McConnell.

By Thursday evening, the Kentucky conservative had resumed pummeling Obama. In a statement that commended the deal he’d helped broker, McConnell assailed the president for stirring up the political acrimony Obama has publicly decried. “The president’s statements castigating House Republicans have thus amounted to the kind of unhelpful political opportunism Americans are tired of,” McConnell said.

The only reason a payroll tax holiday and an extension of unemployment insurance are necessary, the minority leader added (not for the first time), is because of Obama’s “failure to turn our nation’s economy around nearly three years into his administration.”

Thursday’s developments are really agreements hanging by gossamer threads. Stay tuned.