Quickly pivoting the political conversation from President Obama’s reelection to Washington’s looming budget battles, House Speaker John A. Boehner on Wednesday offered a potential path to compromise, saying Republicans are “willing to accept new revenue” to tame the soaring national debt and avert an ugly battle over the approaching “fiscal cliff.”

With Obama’s decisive electoral victory and Republicans’ hold on the House, with a slightly smaller majority, Boehner (R-Ohio) said Tuesday’s election amounted to a plea from voters for the parties to lay down their weapons of the past two years and “do what’s best for our country.”

“That is the will of the people. And we answer to them,” Boehner said at an afternoon news conference at the Capitol. “For purposes of forging a bipartisan agreement that begins to solve the problem, we’re willing to accept new revenue, under the right conditions.”

In phone calls made overnight and this morning from Chicago, Obama said much the same thing to Boehner, Senate Majority Leader Harry Reid (D-Nev.), Senate Minority Leader Mitch McConnell (R-Ky.) and House Minority Leader Nancy Pelosi (D-Calif.). He said he believed that the American people sent a message that leaders in both parties need to put aside their partisan interests and work with common purpose to put the interests of the American people and the American economy first.

While Boehner suggested that Republicans would still oppose Obama’s plan to take “a larger share of what the American people earn through higher tax rates,” he said the party is open to “increased revenue . . . as the byproduct of a growing economy, energized by a simpler, cleaner, fairer tax code, with fewer loopholes, and lower rates for all.”

It was not immediately clear whether Boehner meant that Republicans 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 generate revenue by improving the economy, an assertion that budget analysts say is difficult to measure. Democrats have insisted that any deal must include tax code changes that would add to government coffers whether or not they help the economy.

But Boehner hinted that he is open to the latter, citing a Republican offer during the negotiations of the congressional supercommittee last fall, as well as his own negotiations with Obama during the 2011 debt-limit battle. At that time, Boehner had tentatively agreed to support $800 billion in additional revenue over the next decade in exchange for Obama’s commitment to let the top tax rate fall below the current 35 percent. Obama and other Democrats have long insisted that the George W. Bush-era tax cuts should be permitted to expire for the nation’s top earners, raising the top rate to 39.6 percent.

Boehner mentioned his negotiations with Obama in the speech Wednesday, saying: “We’re closer than many think to the critical mass needed legislatively to get tax reform done.”

In exchange, however, Boehner said Democrats must not “continue to duck the matter of entitlements,” referring to the rising cost of Social Security and federal health programs, which he called “the root of the problem.”

Boehner offered no details about the scope of GOP demands to rein in those programs. But he suggested a model for negotiations in the legislative session scheduled to begin Tuesday, proposing that policymakers enact a deficit-reduction plan aimed at replacing about $100 billion in automatic spending cuts set to kick in at the end of the year. This plan should be coupled with a framework for broader tax and entitlement reforms next year, in his view.

“We won’t solve the problem of our fiscal imbalance overnight, in the midst of a lame duck session of Congress. And we certainly won’t solve it by simply raising tax rates or taking a plunge off the fiscal cliff,” he said. “What we can do is avert the cliff in a manner that serves as a downpayment on — and a catalyst for — major solutions, enacted in 2013, that begin to solve the problem.”

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 election results were in Tuesday night, the president 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 split 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 Hispanics — a key and expanding demographic -- was overwhelming: About seven in every 10 voters sided with the president after Romney repeatedly promised 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, the balance of power in Washington remained largely intact, raising the spectre of an immediate return to budget gridlock.

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.

“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 then 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.”

Zachary A. Goldfarb and Marc Fisher contributed to this report.