President Barack Obama didn’t get much out of the initial two-month deal to extend his payroll tax holiday. But the revolt by House Republicans against the Senate-passed measure gave the White House a chance Monday to portray the GOP as being taken over by a fringe that is willing to risk a tax increase on every worker.

For the White House, it’s a simple political win-win — Obama takes credit if the tax cut gets extended or pins the blame on the GOP if it doesn’t.

“Blowing up the process right now is playing politics with the payrolls of 160 million Americans,” White House Press Secretary Jay Carney told reporters Monday.

While the White House desperately wants the payroll tax cut to be extended — it sees it as a critical political and economic victory ahead of the November elections — it also believes the public will punish House Republicans if a tax hike occurs after 89 Senators voted to prevent one.

The White House was as stunned as anyone when House Republicans balked at the deal, sources said. Obama himself had declared it a victory Saturday for the middle class.

Indeed, senior administration officials Saturday talked about the bill as a done deal, one they contended would benefit them politically because they believed Republicans would be hard-pressed not to continue the tax cut and unemployment benefits come February — in the midst of an election year. But while they talked up the bill, it is far from a slam dunk for the president. It provided about $30 billion of the $447 billion he called for in his American Jobs Act and didn’t fund any of the new initiatives and tax cuts he proposed.

The Saturday spin from the White House also belied the vulnerabilities the measure would create for Obama. It fell short of his goal for a full-year extension, and there was no guarantee he would have the political upper hand on the issue come February. Plus, the deal, which included an imperative for the president to act on the controversial Keystone XL pipeline, would put him in an uncomfortable position two months from now when he would be forced to decide between union backers of the pipeline project and environmentalists who oppose it. It also included provisions that could make mortgages more expensive to refinance.

But Obama now has a bipartisan compromise in hand and a GOP bogeyman to blame for its potential failure.

After all, Obama personally called and thanked Senate Minority Leader Mitch McConnell (R-Ky.) and Majority Leader Harry Reid (D-Nev.) for working out a bipartisan compromise.

But in another sign of Obama’s aloof relations with Hill Republicans, he did not call Speaker John Boehner (R-Ohio) before or after making his “victory” statement.

“Not only did the Speaker not tell the White House or Senate leaders, for that matter, that he’d support the two-month deal, our office has had no communication with the White House at all on the matter,” Boehner spokesman Brendan Buck said. “Radio silence.”

But Carney countered Monday that “it’s not our job to negotiate between [Boehner] and Senate Republicans,” and he contended that it’s inconceivable that Senate Republicans would vote en masse for a bill without any indication that the skids were greased for it in the House.

He also referred to news reports, denied by Boehner, that the Speaker supported the compromise before getting pushback from his Conference.

The Republican revolt “is simply perplexing to all of us,” Carney said. He suggested that a subsection of House Republicans was running the show and that Boehner doesn’t have control over his Conference.

Carney, however, refused to back up Reid’s threat that the Senate would only negotiate a long-term tax cut deal once the House passed the short-term measure.

Obama “wants Congress to get this done,” Carney said. “He’s been here and will be here.”

As for Reid, Carney said he is “understandably frustrated and perplexed” after negotiating a deal with McConnell only for Boehner to sink it.

Carney was standing in front of countdown clocks showing 12 more days until taxes go up unless Congress acts, although the White House had crossed out “Congress” and replaced that with the “House.”

Carney also pointed out shifting Republican statements on whether to do the payroll tax cut at all and said that if it wasn’t for the president pushing the issue, the tax cut would have died. He cited statements from Republicans opposing it initially, then reluctantly supporting it, and now demanding that it be extended not just for two months, but for the full year.

More broadly, Carney contended the public would be upset if House Republicans block the only deal on the table that would ensure taxes don’t go up.

“The American people overwhelmingly support this,” he said, and “the American people will justifiably be angry” if the tax cut lapses.

House Republicans, meanwhile, sought to use the president’s own words against him and contended the two-month package was designed so that Obama and Democrats could go home for the holidays instead of getting their work done.

A blog post by Boehner’s office pointed to Obama’s statements that “Congress should not go home for vacation until it finds a way to avoid hitting 160 million Americans with a tax hike on January 1st.”

“Like President Obama and several other Democrats, Republicans believe the American people ‘can’t wait’ for Congress to act on a full-year extension of the payroll tax cut,” the post said.