WASHINGTON – The outline of a compromise over impending tax hikes and spending cuts began to come into focus Friday after President Barack Obama convened top congressional leaders at the White House.

Differences remain, especially as Republicans, led in the House by Speaker John A. Boehner of Ohio, continue to fight to keep tax rates for the wealthiest Americans from rising.

But the contours of a two-stage deal are taking shape as leaders work to avert a year-end fiscal crisis and break the gridlock that has soured voters on Washington. The mood alone, with Obama congratulating Boehner on his birthday Saturday and Republican and Democratic leaders taking turns speaking to signify their unity, signaled a sharp change from past confrontations.

“We have the cornerstones of being able to work something out,” said Senate Majority Leader Harry Reid of Nevada, as leaders from both parties emerged from the White House. “This is not something we’re going to wait until the last day of December to get done. We have a plan. We’re going to move forward on it.”

Boehner, who presented his framework for a broad tax-and-spending overhaul to be undertaken in 2013, also sounded an optimistic note.

“To show our seriousness, we’ve put revenue on the table, as long as it’s accompanied by significant spending cuts,” Boehner said. “It’s going to be incumbent on my colleagues to show the American people we’re serious.”

The first part of such a deal would be legislation this year that would commit Congress to specific revenue increases, favored by Democrats, and spending cuts, as advocated by Republicans. How those increases and cuts would be achieved would be worked out in the second stage next year by the new Congress.

Not addressed was how to resolve the standoff over this year’s expiring tax rates. Resolving the tax breaks for wealthy Americans remains, in many ways, the linchpin to a deal.

Obama and Boehner appeared more comfortable together than a year ago, when they tried — and failed — to reach a $4 trillion deficit-reduction deal that many economists have warned is vital for the nation’s long-term fiscal health.

The two leading actors exchanged a light moment as the president wished the speaker, who turns 63 on Saturday, a happy birthday and gave the known Merlot fan an expensive bottle of Italian red wine.

“My hope is this is going to be the beginning of a fruitful process that we’re able to come to agreement on that will reduce our deficit in a balanced way, that we will deal with some of these long-term impediments to growth, and we’re also going to be focusing on making sure that middle-class families are able to get ahead,” Obama said as he opened the meeting in the Roosevelt Room. “We’re going to get to work.”

Friday’s closed-door gathering was the first such sit-down since the election, which emboldened Obama and his allies on Capitol Hill. Americans spoke at the polls, they maintain, preferring the Democratic approach, which asks the wealthiest taxpayers to contribute more revenue while preventing steep spending to domestic cuts.

To rank-and-file Republicans, though, the election results signaled that voters want the Republican House majority to hold a final “line of defense,” as Boehner puts it, against what they see as government overreach.

Efforts to raise new tax revenue while cutting spending has eluded the parties in the past, but this year’s built-in deadline could give them a boost.

Unless Congress acts, taxes will rise on most Americans, a $2,000 average hit as current rates expire on Dec. 31. Massive federal spending cuts scheduled to begin Jan. 2 would cut across defense and domestic accounts, pulling funds out of the economy. Together, they have been referred to as a “fiscal cliff.”

A shift can be heard in the rhetoric, as Republicans now say they are willing to consider increases in tax revenue, and Obama has softened his insistence that top income tax rates, now at 35 percent, must rise to 39.6 percent, the rate from the Clinton era.

“We all understand where we are,” said Sen. Mitch McConnell of Kentucky, the Republican leader. “We’re prepared to put revenue on the table provided we fix the real problem, even though most of my members, I think without exception, believe that we’re in the dilemma we’re in not because we tax too little but because we spend too much.”

During the hourlong session Friday, Boehner presented his proposal to have the parties agree to “targets” for new tax revenues and spending cuts, which would be bound by statute and enacted in 2013.

Tax revenue could be raised by closing tax loopholes or capping deductions for the wealthiest Americans — couples earning incomes above $250,000, or $200,000 for singles. Such a broad deal would also require Democrats to agree to rein in spending on Medicare, Medicaid and other entitlement programs as Obama has previously proposed.