Hours after Barack Obama’s soaring victory speech and a gracious concession by Mitt Romney, Republican leaders in Washington made clear Wednesday that whatever mandate the president won for his second term will be sharply limited by the losing party’s starkly different view of the nation’s challenges.

After an election in which the nation essentially ratified the status quo — keeping an embattled but broadly admired president, a Democrat-controlled Senate and a Republican-run House — Obama called for healing and cooperation on key issues such as the deficit, tax reform and immigration.

But Senate Minority Leader Mitch McConnell (R-Ky.), who said during the president’s second year in office that his party’s chief objective was to make Obama a one-term president, quickly announced that “the voters have not endorsed the failures or excesses of the president’s first term.” He urged Obama “to propose solutions that actually have a chance of passing the Republican-controlled House.”

House Speaker John A. Boehner (R-Ohio) said Wednesday that Republicans are “willing to accept new revenue” to pull the nation back from the end-of-year fiscal cliff. He said the election was a plea from voters for both parties to step out of their corners and “do what’s best for our country,” adding, “That is the will of the people. And we answer to them.”

“For purposes of forging a bipartisan agreement that begins to solve the problem, we’re willing to accept new revenue, under the right conditions,” he said. But Boehner said Republicans would continue to oppose Obama’s plan to take “a larger share of what the American people earn through higher tax rates.”

It was not clear whether Boehner would acquiesce only to fresh revenues generated through economic growth, rather than actual tax increases. Republicans have long argued that reforming the tax code would produce new revenue by improving the economy, a claim budget analysts say is difficult to assess. Democrats have insisted that any deal include changes to the tax code that would guarantee additional income to the government.

Senate Majority Leader Harry M. Reid (D-Nev.) said he spoke to Boehner and that they agreed not to “draw lines in the sand” on taxes. Reid said he is ready to “dance” with the other party, but would “fight” if necessary, and he said he would counter obstructionism with an effort to change the Senate’s filibuster rules to limit the minority’s power to block legislation.

On Wall Street, a sell-off gained momentum at midday, with the Dow Jones industrial average falling below 13,000 for the first time since September, as investors focused on the coming showdown over the fiscal cliff, as well as gloomy projections about Europe’s economic growth. Many corporate leaders had supported Romney as the more business-friendly candidate.

Less than two months remain before the fiscal cliff, when big tax increases and draconian spending cuts kick in on Jan. 1 unless Obama and Congress forge a budget deal. The president and legislators enter those negotiations elbows out, with each side claiming support from a country that remains politically split in half.

Overnight and Wednesday morning, Obama called Boehner, McConnell, Reid and House Minority Leader Nancy Pelosi (D-Calif.), urging them to join him in seeking to reduce the deficit, cut taxes for middle class families and create jobs.

Soon after dawn Wednesday, Republicans began explaining their loss to themselves and the nation, as competing engines of recrimination, reconciliation and reexamination started churning.

Some conservatives suggested doubling down on the culture wars, sticking with a hard line on abortion, marriage and other social issues. Other Republicans said Hurricane Sandy contributed to their defeat, arguing that the storm gave Obama a chance to demonstrate government’s good side and distracted voters from Romney’s message.

But some conservative politicians and commentators said the shape of the president’s victory demonstrated that Republicans have painted themselves into a demographic corner — alienating Hispanic voters with harsh rhetoric on immigration and pushing away young voters with a hard line on gay marriage and reproductive rights. The result, some said, is an emerging Democratic majority based on non-whites, singles, young people and the professional class.

The nation’s racial and ethnic makeup is shifting in ways the Daily Caller described as “profound.” It added: “They’re also permanent and likely to accelerate. In order to remain competitive outside Utah, the GOP will have to win new voters, and soon.”

“We have a period of reflection and recalibration ahead for the Republican Party,” said Sen. John Cornyn (R-Tex.), chairman of the National Republican Senatorial Committee.

For their part, Democrats argued that the election was a decisive defeat for tea party Republicans and their hard line against tax increases. “The Tea Party is over,” crowed a statement from the Democratic Congressional Campaign Committee, pointing to the defeat of more than a dozen Republican House incumbents, including several prominent tea party adherents.

Boehner framed Tuesday’s results as a victory for House Republicans. “The American people want solutions — and tonight, they’ve responded by renewing our majority,” he told the Republican National Committee in comments also published on his blog. “With this vote, the American people have also made clear that there is NO mandate for raising tax rates.”

The White House made clear that Obama begs to differ. An administration official argued Wednesday that the election results validate Obama’s view that tax cuts benefiting wealthy Americans must be allowed to expire.

The official said the president, as he signaled in his victory speech, wants to work with Republicans, but believes he now has a mandate to raise taxes on high-income earners.

Most voters agree with Obama’s approach, according to exit polling. Forty-seven percent of voters polled said taxes should be increased only on Americans earning at least $250,000 per year — the president’s view; an additional 13 percent said they should be raised for everyone. Thirty-five percent favored no tax increases for anyone, mirroring the Republican position.

The administration official pointed to support for higher taxes on top earners from corporate leaders such as Honeywell chief executive David Cote. But other business groups, such as the U.S. Chamber of Commerce, oppose such increases.

Obama is proposing about $1.5 trillion in new tax revenue over a decade, largely by raising rates to 39.6 percent for wealthy Americans and eliminating tax deductions and loopholes.

On MSNBC before the vote, Obama said he would interpret a win as “a mandate for doing it in a balanced way. We can do some more cuts. We can look at how we deal with the health-care costs in particular under Medicare and Medicaid in a serious way. But we are also going to need some revenue.”

Exit polling Tuesday showed that more than half of Americans believe the economy is poor or worsening, and the nation remains sharply divided on whether government should do more or is already doing too much.

Well more than half of those polled said they trust Obama in a crisis. But the president’s support came from an America very much divided by geography, race, religion and sex, according to exit poll data.

Obama won the Northeast and West Coast, while Romney took the South and much of the nation’s midsection. Obama won large majorities among black, Hispanic, Asian and multiracial voters; Romney easily carried the white vote. Obama’s haul among a key and expanding demographic, Hispanics, was overwhelming: about seven in every 10 voters sided with the president after Romney’s repeated promise to adopt policies that would get illegal immigrants to “self-deport.”

Romney won among Protestants; the president found majorities among Catholics, Jews and members of other faiths. Men sided more with Romney; women solidly favored Obama.

After billions of dollars in campaign spending, more than a year of fiery rhetoric and four years of stubbornly high unemployment, Democrats made only slight gains in each chamber of Congress.

Obama, 51, scored his decisive electoral college victory by stringing together narrow wins in hotly contested states. The president won at least five of this year’s seven major battleground states; Romney beat him in North Carolina, and Florida remains too close to call. But Obama’s popular vote win was slim, reflecting a nation that remains deeply divided.

The president acknowledged and even embraced that division in a victory speech at 1:40 a.m. Eastern time that was as rhetorically ambitious as his first debate performance was mediocre.

“I know that political campaigns can sometimes seem small, even silly,” he said, before making the counterargument that passions and controversy can be a good thing. “These arguments we have are a mark of our liberty.”

Obama reached out to Romney, saying he would seek to consult with his challenger, and to Republicans, asking them to work with him to reduce the deficit, reform the tax code and fix the nation’s immigration system.

“We can seize this future together because we are not as divided as our politics suggests,” Obama told ecstatic supporters in the cavernous McCormick Place Lakeside Center in Chicago. “We’re not as cynical as the pundits believe. We are greater than the sum of our individual ambitions, and we remain more than a collection of red states and blue states.

“We are and forever will be the United States of America.”

The presidential vote capped a night of gains for the once beaten-down American left. Democrats Tammy Baldwin in Wisconsin and Elizabeth Warren in Massachusetts won Senate races, making Baldwin the nation’s first openly gay senator. Maryland and Maine became the first states to legalize same-sex marriage by popular vote, and Minnesota rejected a constitutional ban on same-sex marriage. Colorado and Washington passed laws legalizing some marijuana use.

Democrats widened their majority in the Senate by two seats; the next Senate will have 53 Democrats, 45 Republicans and two independents, both of whom are expected to align with the Democrats. GOP Rep. Rick Berg Wednesday afternoon conceded to Democrat Heidi Heitkamp in the race for an open Senate seat in North Dakota. Sens. Dean Heller (R-Nev.) and Jon Tester (D-Mont.) also squeezed out victories Wednesday.

Rep. Michelle Bachmann (R-Minn.) won her tight race in late tallying, leaving one race too close to call. Rep. Allen West (R-Fla.) was neck-and-neck with challenger Patrick Murphy, separated by only about 2,500 votes and possibly headed to a recount.

Romney, a former Massachusetts governor, had built his campaign around the contention that the U.S. economy is battered and adrift because of Obama’s failures, and that his own business experience uniquely qualified him to fix it.

In the end, that wasn’t enough, in part because the economy undermined his argument by showing signs of improvement. Just weeks before Election Day, the national unemployment rate dropped below 8 percent for the first time since Obama took office.

Voters never warmed to Romney. Even after many months and millions of dollars devoted to portraying him as a strong manager with a plan to put Americans back to work, exit polls showed that just as many voters trusted Obama to handle the economy as trusted the former Bain Capital executive.

“This is a time of great challenges for America, and I pray that the president will be successful in guiding our nation,” a slightly hoarse Romney told supporters in Boston early Wednesday. He said he and his running mate, Rep. Paul Ryan (Wis.), had left “everything on the field,” adding: “I so wish that I had been able to fulfill your hopes.”

Ryan, who ran simultaneously to become vice president and for another term in Congress, was reelected to his House seat and said he would seek to remain as budget committee chairman.

As of Wednesday morning, Florida remained too close to call, although Obama maintained a narrow lead. But the outcome in that state became irrelevant to the national contest, as Obama easily passed the threshold of 270 electoral votes with victories in Ohio, Virginia and other battlegrounds.

Romney was beaten by a different Obama than the one who defeated Republican Sen. John McCain (Ariz.) four years ago. Back then, Obama had run as a symbol of limitless hope.

This year, he ran as a symbol of hope’s limitations.

The president no longer pledged to sweep away Washington’s old partisan politics. He had tried that and was unable to do so. Instead, during the campaign, he pledged to plunge into those old politics and fight — battling Republicans whom Obama said favored the rich and waged a “war on women.”

So now, ironically, the bruised Obama of 2012 has the job that the hopeful Obama of 2008 said he wanted: to conjure “change” out of a capital that is split and paralyzed by partisan battling.

For Romney, 65, Tuesday’s loss ends a personal marathon that began in June. But, in a broader sense, it started with his first presidential run, nearly six years ago. A longtime executive and investor, Romney ran a campaign that promised to bring a businessman’s clear-eyed conservatism to the problems of the economy.

He was helped immensely by a new breed of political action group, the free-spending super PACs that the Supreme Court legalized in 2010. Outside groups, including super PACs, poured an estimated $350 million into the race on his behalf, with pro-Obama groups spending an estimated $100 million.

For Romney’s family, it was the third unsuccessful attempt to capture the White House: Romney's father, George Romney, a Republican governor of Michigan, ran in 1968.

But the upward course of the son’s campaign was a cold kind of victory. He had spent years fighting a perception that he was too moderate, too malleable for the swashbuckling, tea-partying modern GOP. In this campaign’s final days, he became a bona-fide Republican hero.

At recent rallies, as many as 30,000 people roared his name. On Tuesday, during a last-minute trip to Pennsylvania, Romney stepped off his campaign plane in Pittsburgh and was surprised to see supporters cheering him from a parking garage.

Romney appeared moved and waved back without speaking. “That’s when you know you’re going to win,” he told a reporter.

Romney’s candidacy was also a milestone for his religion, the Church of Jesus Christ of Latter-day Saints. Mormons, once persecuted to the desert edge of American civilization, now have 15 members in Congress and something that few American minority groups can point to, a credible run for the nation’s highest office in which their faith was barely mentioned as an issue.

Obama strategists pointed to three of the president’s actions as decisive moments in building his victory.

His controversial bailout of the U.S. auto industry won favor among nearly six in ten voters in the crucial battleground state of Ohio, exit polls showed, apparently helping him fare better than usual there among a group he has consistently lost by a lot: white men without a college education.

Obama’s choice to offer some young illegal immigrants who were brought to the United States as children the temporary right to live and work in this country legally helped him win 60 percent of Latino voters in Florida, up three percentage points from four years ago, exit polls showed.

And Obama’s handling of Hurricane Sandy, which earned him plaudits from New Jersey Gov. Chris Christie (R), a major Romney backer, was cited by four in ten voters as an important factor in their vote: More than 60 percent of those who said that voted for the president.

Obama’s victory seems to guarantee that the landmarks of his first term — the Dodd-Frank financial reforms and the health-care law — will remain in effect. Romney had promised to repeal both.

Obama did not announce a broad new theme in his victory address or his campaign. Instead, his vague slogan, “Forward,” was a sign that the election was about voters trusting him, rather than specific ideas. But the president early Wednesday did name four areas on which he intends to push: deficit reduction, tax reform, immigration and energy independence, all parts of the “nation-building at home” that he promised to focus on after winding down the wars in Iraq and Afghanistan.

Zachary Goldfarb, Lori Montgomery, Robert Barnes, Jon Cohen and Nia-Malika Henderson in Washington; Darryl Fears in Manchester, N.H.; Stephanie McCrummen in Boston; Felicia Sonmez in Pittsburgh; Susan Svrluga in Arlington; and Craig Timberg in Cleveland contributed to this report.