WASHINGTON — An economic calamity looming, President Barack Obama on Friday signaled willingness to compromise with Republicans, declaring he was not “wedded to every detail” of his tax-and-spending approach to prevent deep and widespread pain in the new year. But he insisted his re-election gave him a mandate to raise taxes on wealthier Americans.

“The majority of Americans agree with my approach,” said Obama, brimming with apparent confidence in his first White House statement since securing a second term.

Trouble is, the Republicans who run the House plainly do not agree with his plans. Speaker John Boehner insisted that raising tax rates as Obama wants “will destroy jobs in America.”

So began the “fiscal cliff” political maneuvering that will determine which elected power center — the White House or the House — bends more on its promises to voters. The outcome will affect tens of millions of Americans, given that the tax hikes and budgets cuts set to kick in Jan. 1 could spike unemployment and bring on a new recession.

An exhausting presidential race barely history, Washington was back quickly to governing on deadline, with agreement on a crucial goal but divisions on how to get there. The campaign is over, but another has just begun.

The White House quickly turned Obama’s comments into an appeal for public support, shipping around a video by email and telling Americans that “this debate can either stay trapped in Washington or you can make sure your friends and neighbors participate.”

Obama invited the top four leaders of Congress to the White House next week for talks, right before he departs on a trip to Asia.

In laying their negotiating markers, all sides sought to leave themselves wiggle room.

“I don’t want to box myself in. I don’t want to box anybody else in,” Boehner said at the Capitol.

Outside all the new the talk of openness, the same hard lines seemed in place.

Obama never expressly said that tax rates on top earners must return to the higher levels of the Bill Clinton era, leading to speculation that he was willing to soften the core position of his re-election campaign to get a grand debt deal with Republicans. “I’m not wedded to every detail of my plan. I’m open to compromise,” he said.

But his spokesman, Jay Carney, seemed to slam that door. He said Obama would veto any extension Congress might approve of tax cuts on incomes above $250,000.

Obama’s remarks were choreographed so that a diverse-looking group of Americans stood behind him and dozens more were invited to pack the East Room. In the weeks ahead, he plans to pull in the public as a way to pressure Congress.

“I am not going to ask students and seniors and middle class families to pay down the entire deficit while people like me, making over $250,000, aren’t asked to pay a dime more in taxes. I’m not going to do that,” said Obama.

He said voters plainly agreed with his approach that both tax hikes and spending cuts are needed to cut the debt.

“Our job now is to get a majority in Congress to reflect the will of the American people,” Obama said.

About 60 percent of voters said in exit polls Tuesday that taxes should increase, either for everyone or those making over $250,000. Left unsaid by Obama was that even more voters opposed raising taxes to help cut the deficit.

The scheduled year-end changes, widely characterized as a dangerous “fiscal cliff,” include a series of expiring tax cuts that were approved in the George W. Bush administration. The other half of the problem is a set of punitive across-the-board spending cuts, looming only because partisan panel of lawmakers failed to reach a debt deal.

Put together, they could mean the loss of roughly 3 million jobs.

Since the election, Boehner and Obama have both responded to the reality that they need each other.

Compromise has become mandatory if the two leaders are to avoid economic harm and the wrath of a public sick of government dysfunction.

Obama says he is willing to talk about changes to Medicare and Medicaid, earning him the ire of the left. Boehner says he will accept raising tax revenue and not just slashing spending, although he insists it must be done by reworking the tax code, not raising rates. The framework, at least, is there for a broad deal on taxes.

Yet the top Democrat and Republican in the nation are trying to put the squeeze on each other as the public waits for answers.

“This is his opportunity to lead,” Boehner said of Obama, not long before the president said: “All we need is action from the House.”

Obama said the uncertainty now spooking investors and employers will be shrunk if Congress extends — quickly — the tax cuts for all those except the most-well off.

The Senate has passed such a bill. The House showed no interest on Friday in Obama’s idea.

Obama and Republicans have tangled over the Bush tax cuts for years. The president gave in to Republican demands to extend the cuts across the board in 2010, but he ran for re-election on a pledge to allow the rates to increase on families making more than $250,000 a year.

Also lurking is the expiration of the nation’s debt limit in the coming weeks. The last fight on that nearly led the United States to default on its bills.

When asked if he would try to use that issue as leverage, Boehner said it must be addressed “sooner rather than later.”

The national debt now stands above $16 trillion. The government borrowed about 31 cents of every dollar it spent in 2012.