WASHINGTON » Leaders of Congress declared confidence today they could reach a deal with President Barack Obama to avert economically convulsive tax increases and budget cuts at year’s end, in a rare show of unity reflecting the dire stakes in a nation sick of political stalemate.

"I believe that we can do this," House Speaker John Boehner, R-Ohio, said after top lawmakers met with Obama at the White House.

Significantly, the same tone emerged from every corner of divided government— Obama spokesman Jay Carney, top Senate Republican Mitch McConnell, top House Democrat Nancy Pelosi, and Senate Majority Leader Harry Reid.

And while all sides sought to assure weary American consumers, edgy investors and wary employers that the nation would not plunge over the "fiscal cliff" come Jan. 1, they furnished precious few details on how they planned to proceed.

"We understand our responsibility," said Pelosi, D-Calif. "I feel confident that a solution may be in sight."

That solution exists only in the broadest sense, with Republicans conceding that any bargain to cut the debt must include tax revenue, and Democrats acknowledging there must be spending cuts to a host of major programs relied upon by millions of Americans.

Any solution likely would come in two phases, with steps now to avert a crisis and promises of a broader tax reform process in 2013.

None of the lawmakers made any mention of a big sticking point — Obama’s insistence that tax rates go up, as scheduled, at the start of the year for individuals making over $200,000 a year and families earning over $250,000. Republicans flatly oppose that proposal.

At issue are a broad series of looming tax increases across every income bracket, coupled with across-the-board spending cuts. The gritty work of negotiations is now under way, and the White House work on this matter will be carried on by staff members as Obama heads off to Asia on Saturday.

The president made a point of sounding — and looking — like a man willing to compromise.

He joked with Boehner about his 63rd birthday on Saturday and later gave him a bottle of Italian wine.

Obama said the goal was to prevent a tax hike for middle-class families, create jobs and keep the economy growing.

"That’s an agenda that Democrats and Republicans and independents, people all across the country share," Obama said. "So our challenge is to make sure that we are able to cooperate together, work together, find some common ground."

Boehner said he put forward a plan that meets Obama’s goals of "balance."

"To show our seriousness, we’ve put (tax) revenue on the table, as long as it’s accompanied by significant spending cuts," Boehner said later. McConnell, R-Ky., agreed but said his members believe too much spending, not too little taxing, is the problem.

Reid, D-Nev., said any deal will not come down to the end of December.

"There is no more, ‘Let’s do it some other time,’ " he said. "We’re going to do it now. We feel very comfortable with each other."

Vice President Joe Biden, Treasury Secretary Timothy Geithner and top White House advisers also took part in the Roosevelt Room meeting.

Said Obama: "My hope is that this is going to be the beginning of a fruitful process."

In news conferences and other public statements, Obama and the congressional leaders have been setting negotiating markers for a debt deal. The session at the White House was their first meeting together since the election, one in which Obama says the American people voted for his way to cut the debt.

Obama has insisted that any deal involve higher taxes on the top 2 percent of income earners. Republicans leaders are vowing to resist rate hikes as job-killers, though they’ve signaled they’re open to added revenue through curbs on deductions and credits.

This afternoon, Obama will continue his efforts to build a coalition of support for his position when he and Biden meet with leaders of civil rights and other organizations. Obama has already met with leaders of labor and liberal organizations as well as corporate CEOs who have backed his call for greater tax revenue.

At issue is a one-two punch of expiring Bush-era tax reductions and across-the-board spending cuts set to hit in January as self-imposed punishment for the failure of a gridlocked Congress to reach a deficit-cutting deal last year.

The White House says Obama’s starting point for negotiations is his February budget plan, which combined $1.6 trillion in new revenues over the coming decade — chiefly from upper-income earners — with modest cuts to benefits programs. Obama’s plan promises $4.4 trillion in deficit cuts over 10 years, but more than half of that would come by banking already accomplished cuts and questionable savings from winding down military operations in Iraq and Afghanistan.

In the run-up to the meeting, Obama has been firm that taxes are going up on upper-bracket earners, though Boehner and McConnell are adamant that his campaign promise of raising the top income tax rate on family income exceeding $250,000 a year is a non-starter.

The bargaining landscape has shifted markedly in Obama’s favor since his failed talks with Boehner, R-Ohio, in the summer of 2011 on a "grand bargain" on the budget.

Then, Obama squared off against a tea party-driven House on the need to extend the government’s ability to borrow to avoid a market-crunching first-ever default on its debt obligations. Now newly re-elected, Obama is putting Republicans on notice that he’s willing to mount a national campaign blaming them for holding up renewed tax cuts for most with an ultimatum against renewing them for top income earners.

AP writers Jim Kuhnhenn and Matthew Daly contributed to this report.