The House speaker, John A. Boehner of Ohio, striking a conciliatory tone a day after the Republican Party's electoral drubbing, said on Wednesday that he was ready to accept a budget deal that raises federal revenue as long as it is linked to an overhaul of entitlements and a reform of the tax code that closes loopholes, curtails or eliminates deductions and lowers income tax rates.
Mr. Boehner's gesture was the most explicit offer he has made to avert the "fiscal cliff" in January, when billions of dollars in tax increases and automatic spending cuts go into force. And it came hours after Senator Harry Reid of Nevada, the majority leader, offered his own olive branch, saying "it's better to dance than to fight."
"Mr. President, this is your moment," Mr. Boehner told reporters in the Capitol. "We're ready to lead, not as Democrats or Republicans, but as Americans."
The offer may be enough to bring the parties to the table in the wake of an election that kept President Obama in power, strengthened the Democrats' grip on the Senate and chipped away at the still-large Republican majority in the House.
But Democrats and Republicans are still far apart. Mr. Boehner made it clear that his vision for additional revenue includes a tax code that lowers even the top income tax rate from where it is now, 35 percent, not where it would be in January when the Bush-era tax cuts are set to expire -- 39.6 percent. At least some of that additional revenue would come from economic growth that he said would be fueled by a simpler tax code.
Senator Charles E. Schumer of New York, the third-ranking Democrat, has said those constructs are unacceptable. Democratic leaders say tax reform that lowers tax rates across the board would either hurt the middle class by trimming vital tax benefits like the home mortgage deduction or would not raise enough taxes to meaningfully reduce the deficit. Mr. Reid underscored Mr. Obama's contention that tax rates on the rich must rise, saying "the vast majority of Americans" support that, "including rich people."
But in language and timing, the leaders of Congress's two chambers left the unmistakable impression that they want a deal at least large enough to avert the worst economic impacts of a sudden rise in income, payroll, capital gains, dividend, interest and estate tax rates that would affect virtually every American family, working or not. Mr. Boehner has said for months that a deal to reform taxes and entitlements and substantially lower the deficit is not appropriate for a lame-duck Congress.
But facing a Congress next year that will be less Republican than the current one, he suggested on Wednesday that he would favor a deal that would serve at least as "a down payment on -- and a catalyst for -- major solutions, enacted in 2013."
He said he had spoken to the president on Wednesday before making his statement to reporters.
"I'm not suggesting we compromise on our principles," he said, "but I am suggesting we commit ourselves to creating an atmosphere where we can see common ground when it exists and seize it."
Mr. Obama enters the next fray with heightened leverage, both sides agree, especially on what he sees as the most immediate issue: Whether Republicans will relent and extend the Bush-era income tax cuts, which expire Dec. 31, except for households with taxable income above $250,000 a year.
Yet if Mr. Obama received a mandate for nothing else after a campaign in which he was vague on second-term prescriptions, he can and will claim one for the proposition that the wealthiest Americans like himself and Mitt Romney should pay higher income taxes. That stance was a staple of Mr. Obama's campaign stump speeches for more than a year. And in surveys of those leaving the polls on Tuesday, voters overwhelmingly agreed with him.
"This election tells us a lot about the political wisdom of defending tax cuts for the wealthy at the expense of everything else," a senior administration official said early on Wednesday.
In his victory speech, Mr. Obama offered what the White House intended as an early olive branch. "In the coming weeks and months," he said, "I am looking forward to reaching out and working with leaders of both parties to meet the challenges we can only solve together: reducing our deficit, reforming our tax code, fixing our immigration system, freeing ourselves from foreign oil."
Much pre-election speculation held that a result like what occurred -- essentially maintaining the status quo with Mr. Obama in the White House; Democrats in control of the Senate, though now with an unexpectedly padded majority; and Republicans still leading the House -- would make for continued gridlock and a fall off the fiscal cliff at some cost to the recovery.
Yet there are counter views. For one thing, had Mitt Romney won, the rough consensus in both parties was that he and Congress would have delayed the scheduled imposition of automatic tax increases and spending cuts for at least six months and up to a year to give Mr. Romney time to staff his administration and outline a plan. And that delay would have been compounded by an all but certain standoff between a new president dedicated to cutting taxes deeply, not raising them, and Democrats in Congress intent on getting tax increases on high incomes in exchange for their assent to future reductions in Medicare and Medicaid.
Also, as the administration and a few other optimists in both parties see it, with the same division of power, the two sides can immediately take up where they left off in 2011. That year, repeated efforts for a bipartisan budget deal ultimately collapsed on the tax issue and on Democrats' refusal to consider reductions in the fast-growing entitlement programs like Medicare and Medicaid unless Republicans compromised.
Each side said the voters would decide in November 2012. Now they have, and Mr. Obama and the two parties in Congress can get back to the bargaining table, where their differences remain in place but so, too, do some tentative agreements on spending cuts. Had Mr. Romney won, the two sides would have faced months of start-from-scratch, get-acquainted bargaining, farther apart than ever on the matter of taxes and entitlement benefits.
Mr. McConnell, in his statement congratulating Mr. Obama early Wednesday, said, "Now it's time for the president to propose solutions that actually have a chance of passing the Republican-controlled House of Representatives and a closely divided Senate."
He added: "To the extent he wants to move to the political center, which is where the work gets done in a divided government, we'll be there to meet him halfway. That begins by proposing a way for both parties to work together in avoiding the 'fiscal cliff' without harming a weak and fragile economy, and when that is behind us, work with us to reform the tax code and our broken entitlement system."
Senator Harry Reid of Nevada, the majority leader, his hand strengthened somewhat, called for Congress to work quickly to resolve the looming fiscal issues in the lame duck session.
"I am going to do anything in my power to be as conciliatory as possible," he said Wednesday in a news conference on Capitol Hill. "I want to work together. But I want everyone also to understand, you can't push us around."
Mr. Reid said the election showed that the public wanted the richest taxpayers to pay more taxes, and he gave no hint of compromise on that matter, perhaps the central point on which the presidential campaign hinged. He also said that a temporary fix for the fiscal impasse was not a good idea.
"I am not for kicking the can down the road," he said. "Waiting for a month, six weeks, six months, that is not going to solve the problem."
John H. Cushman Jr. contributed reporting from Washington.
This article originally appeared in The New York Times.