WASHINGTON » President Barack Obama’s re-election, coupled with Republicans’ continued hold on the House, gives both parties a chance to rethink, and perhaps undo, the bitter partisanship that has gripped Washington for four years and frustrated Americans who see big problems going unsolved.

It won’t be easy. Both sides claim, with some justification, a mandate from the voters.

“We’ll have as much of a mandate as he will,” House Speaker John Boehner, R-Ohio, said shortly before the election, correctly anticipating the results.

Senate Republican leader Mitch McConnell was frostier in his post-election remarks. “The voters have not endorsed the failures or excesses of the president’s first term,” McConnell said. 

“Now it’s time for the president to propose solutions that actually have a chance of passing the Republican-controlled House,” he said, “and deliver in a way that he did not in his first four years in office.”

After three straight swing elections, Americans decided to keep Obama in the White House, leave Republicans in control of the House and let Democrats stay atop the Senate, with Republicans still able to block measures with filibusters.

There’s an irony, or self-flagellation, there. Americans express exasperation at the partisan sniping and gridlock that pushed the nation to the brink of defaulting on its loans last year, and which might trigger new crises soon. The narrowness of Obama’s win accurately reflects the nation’s nearly 50-50 partisan divide. It’s a split that will make progress on any major issues difficult for at least another two years, and probably longer.

Every newly elected president claims a mandate, and Obama can point to the roughly $1 billion that Mitt Romney and his GOP allies spent trying to oust him. Yet, for all its tactical brilliance, Obama’s campaign was built on relatively modest ideas. It focused on helping the middle class, which is a coalition of identity, not ideology.

It may have been a status quo election. But if the White House and congressional Republicans simply stand their ground on taxes and other issues, they run risks — not just for the nation’s well-being, but also for the legacies of a barrier-breaking president and a Republican Party that has tapped a deep vein of conservative, almost libertarian emotion.

In many ways, of course, Obama’s place in history is assured. The first black to be elected president has now joined eight other men who, since 1900, won the office more than once. His biggest first-term achievement — the “Obamacare” health delivery overhaul — is safe from repeal by a President Mitt Romney.

Obama’s other top goals, however, were largely thwarted by a united Republican Party that fought him at almost every turn. Republicans provided not a single House or Senate vote for the health care law. They beat back his efforts to end the Bush-era tax cuts for the wealthiest households.

Obama offered an olive branch in his victory speech early Wednesday. “In the coming weeks and months, I am looking forward to reaching out and working with leaders of both parties to meet the challenges we can only solve together,” he said.

Republican leaders announced four years ago that their top goal was to deny Obama a second term. On Tuesday, they lost, even though the nation’s high unemployment seemed to make Obama ripe for defeat. Some, perhaps much, of Romney’s loss will be traced to Americans’ discontent with an opposition party that refused to compromise on big issues even when it’s obvious that neither party can get everything it wants.

Boehner, Senate Republican leader Mitch McConnell and other GOP officials now must decide where to bend and where to keep standing firm. They’ll have to tip their hand soon. A package of huge tax hikes and spending cuts — known as the “fiscal cliff,” and which both parties deeply dislike — is scheduled to take effect in the new year.

So far, Republicans have adamantly refused to raise taxes, even on the richest Americans, as part of a deficit-reduction package. Obama and other Democrats say such tax hikes must be part of the deal. They will point to Tuesday’s election as validation. Boehner will point to his sustained majority. 

Democrats think Obama learned some hard lessons in his first four years, including a realization that he must get deeply involved in the sometimes unpleasant business of crafting and negotiating legislation.

“The American people have made it pretty clear that they are sick of gridlock and fighting,” said Jim Manley, a former Democratic Senate aide. Boehner and McConnell, he said, “have figured out that the tea party has done enormous damage to their brand, to say nothing about the economy, and that something has to change.”

At the same time, Manley said, “the president is going to have to play a more forceful role in the legislative process.”

Obama signaled some of his second-term goals in a recent Des Moines Register interview. The fiscal cliff’s economic threat is so severe, he said, that a congressional compromise is likely.

“It will probably be messy,” the president said. “But I am absolutely confident that we can get what is the equivalent of the grand bargain that essentially I’ve been offering to the Republicans.” It calls for $2.50 in spending cuts for every $1 in new revenue.

“The second thing I’m confident we’ll get done next year is immigration reform,” he said. Perhaps. Or it could prove as difficult as President George W. Bush’s bid to partly privatize Social Security right after his re-election.

In recent years, the very idea of bipartisan compromise has come under growing attack, as Americans got fed up with soaring deficits, longstanding threats to Medicare and other problems left unresolved by Congress’ old practices. The anger gave birth to the tea party, which boosted candidates who vow not to compromise if they reach Washington.

Passion and ideology drive the tea party. Congressional leaders, historically, are realists. They keep their committee chairmanships and party leadership posts by constantly monitoring the moods and needs of their rank-and-file colleagues.

Some Washington veterans say Boehner is posturing when he claims that his party won as big a mandate as Obama did. When Republicans see that the no-new-taxes argument lost Tuesday, Boehner “is certain to come to the table to begin to deal,” said Matt Bennett of the Democratic-leaning think tank Third Way.

“Boehner and McConnell surely know that they cannot continue to be pure obstructionists and that the economic consequences of going over the fiscal cliff would be extreme,” Bennett said. But it’s not clear they can control their caucuses, he said.

Indeed, the GOP is surely about to engage in some intense self-examination and infighting.

John Feehery, a former top House Republican aide, said Obama’s re-election may give the White House less clout than Democratic insiders think.

“Republicans will feel they have just as big a mandate as the president,” Feehery said. It’s possible that Boehner and Senate Democratic leader Harry Reid of Nevada “will do the deals and put Obama on mute,” he said.

Reid, at least for now, sounds upbeat and bipartisan.

“Democrats and Republicans must come together, and show that we are up to the challenge” of tackling big problems, Reid said after the election was called. “This is no time for excuses.”

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EDITOR’S NOTE — Charles Babington covers Congress and national politics for The Associated Press.