WASHINGTON — One day after a bruising, mixed-verdict election, President Barack Obama and Republican House Speaker John Boehner both pledged Wednesday to seek a compromise to avert looming spending cuts and tax increases that threaten to plunge the economy back into recession.

Added Senate Majority Leader Harry Reid, D-Nev.: “Of course” an agreement is possible.

While all three men spoke in general terms, Boehner stressed that Republicans would be willing to accept higher tax revenue under the right conditions as part of a more sweeping attempt to reduce deficits and restore the economy to full health.

While the impending “fiscal cliff” dominates the postelection agenda, the president and Republicans have other concerns, too.

Obama is looking ahead to top-level personnel changes in a second term, involving three powerful Cabinet portfolios at a minimum.

And Republicans are heading into a season of potentially painful reflection after losing the presidency in an economy that might have proved Obama’s political undoing. They also have fallen deeper into the Senate minority after the second election in a row in which they lost potentially winnable races by fielding candidates with views that voters evidently judged too extreme.

One major topic for GOP discussion: the changing face of America.

“We’ve got to deal with the issue of immigration through good policy. What is the right policy if we want economic growth in America as it relates to immigration?” said former Republican Party Chairman Haley Barbour. Obama drew support from about 70 percent of all Hispanics. That far outpaced Romney, who said during the Republican primaries that illegal immigrants should self-deport, then spent the general election campaign trying to move toward the political middle on the issue.

The maneuvering on the economy — the dominant issue by far in the campaign — began even before Obama returned to the White House from his home town of Chicago.

After securing a second term, the president is committed to bipartisan solutions “to reduce our deficit in a balanced way, cut taxes for middle class families and small businesses and create jobs,” and he told congressional leaders as much in phone calls, the White House said.

Boehner, whose anti-tax Republicans renewed their House majority on Tuesday, said GOP legislators were “willing to accept new revenue under the right conditions.” That means tax reform and economic growth rather than raising rates, he emphasized, and accompanying steps to rein in the government’s big benefit programs.

“The question we should be asking is not ‘which taxes should I raise to get more revenue, but rather: which reforms can we agree on that will get our economy moving again?” the Ohio Republican said at the Capitol.

While both the president and Boehner sent signals of bipartisanship, there remain wide differences between the two on specifics. At the same time, each man has something of a postelection mandate, given Obama’s re-election and the Republicans’ successful defense of their House majority.

The reference to a balanced approach to deficit reduction reflected Obama’s campaign-long call for higher taxes on incomes above $200,000 for individuals and $250,000 for couples.

That was something Boehner made plain he opposes.

Reid told reporters that any solution should include higher taxes on “the richest of the rich.” That was in keeping with Obama’s election platform, which calls for the expiration of tax cuts on higher-income earners.

Barring legislation to avoid the “fiscal cliff” by year’s end, taxes are on course to rise by more than $500 billion in 2013, and spending is to be cut by an additional $130 billion or so, totals that would increase over a decade. The blend is designed to rein in the federal debt, but officials in both parties warn it poses a grave threat to an economic recovery that has been halting at best.

Obama and congressional leaders in both parties say they want an alternative, but serious compromise talks were non-existent during the fierce campaign season.

That ended Tuesday in an election in which more than 119 million votes were cast, mostly without controversy despite dire predictions of politically charged recounts and lawsuits while the presidency hung in the balance.

Obama won the popular vote narrowly, the electoral vote comfortably, and the battleground states where the campaign was principally waged in a landslide.

The president carried seven of the nine states where he, Romney and their allies spent nearly $1 billion on television commercials, winning Ohio, Wisconsin, Iowa, New Hampshire, Nevada, Colorado and Virginia.

The Republican challenger won North Carolina, and Florida remained too close to call

Obama also turned back late moves by Republicans in Pennsylvania, Michigan and Minnesota.

Hispanics account for a larger share of the population than the national average in Nevada and Colorado, two of the closely contested battleground states. The president’s outsized majority among Hispanics — in the range of 70 percent according to Election Day interviews with voters — helped him against a challenger who called earlier in the year for self-deportation of illegal immigrants.

Other factors in crucial states:

— In Ohio, roughly 60 percent of all voters said they favored the Obama administration’s auto bailout, and the president captured nearly three quarters of their votes, according to the survey, conducted for The Associated Press and a group of television networks. He stressed the rescue operation throughout the campaign. Romney opposed it, and in late campaign commercials suggested it had contributed to the loss of U.S. jobs overseas.

— In Virginia, the black vote was roughly half again as big in percentage terms as nationally, also an aid to Obama.

Changes are in store for the victorious administration. The election past, three members of Obama’s Cabinet have announced plans to leave their posts: Defense Secretary Leon Panetta, Treasury Secretary Tim Geithner and Secretary of State Hillary Rodham Clinton. Other changes would not be unusual in the second administration of any president.

As for Congress, Democrats improbably gained seats in re-establishing their Senate majority. Their final margin hinged on a decision by independent Sen.-elect Angus King of Maine, who has not yet said which party he will affiliate with.

There were nine House races that remained too close to call, not counting a Louisiana runoff next month that involves two Republicans. Overall, the GOP secured 234 seats and led for one more, a trend that would translate into a net loss of eight from the current lineup.

In defeat, Democrats pointed to races where they turned tea party-backed conservatives out of power as evidence they had stemmed a tide.

___

Associated Press writers Julie Pace in Chicago and Donna Cassata, Larry Margasak and Andrew Taylor in Washington contributed to this story.