WASHINGTON - President Obama and top Republican congressional leaders - who have had a rocky relationship for two years - insisted Tuesday that they had gotten the midterm election message from voters and began searching immediately for a way to extend Bush-era tax cuts.

The cuts are due to expire Dec. 31. Obama and Democratic congressional leaders want them extended only for individuals earning less than $200,000 a year and couples making less than $250,000. Republicans want the breaks to continue for everyone.

Obama met for about two hours Tuesday with congressional leaders from both parties at the White House, the first time they had met since Republicans won control of the House and gained six Senate seats in Nov. 2 elections.

The tax-cut extension dominated a discussion that also covered expiring unemployment benefits, nuclear arms control, and the push to end the don't ask, don't tell policy for gays in the military.

Obama pushed for quick ratification of New START, and some key Senate Republicans, who had expressed reluctance to approve the arms-control treaty in the lame-duck congressional session, signaled they might relent, saying the administration was doing a good job of addressing their concerns.

"The administration position has continued to evolve in a very positive way," said Sen. Bob Corker (R., Tenn.).

For the final 35 minutes, Obama and congressional leaders asked their staffs to leave the room, a step meant to encourage candor.

The two sides emerged full of praise for each other and, in a sign of urgency, agreed to immediate tax-cut talks among Treasury Secretary Timothy Geithner, Budget Director Jacob Lew, and four key members of Congress.

Even as the group meets, the House could vote Thursday to extend just the middle-class tax cuts, letting cuts for the wealthy expire, said Rep. Chris Van Hollen of Maryland, one of the Democratic congressional negotiators.

"Things can change around here, but the hope would be to try and get something by Thursday," Van Hollen said.

Also representing congressional Democrats will be Sen. Max Baucus of Montana, chairman of the Senate Finance Committee. Republicans will be represented by Sen. Jon Kyl of Arizona, the GOP whip, and Rep. Dave Camp of Michigan, the top Republican on the House Ways and Means Committee.

The two sides seemed ready to tone down the harsh rhetoric that has marked White House-GOP relations since Obama became president 22 months ago. The American people are "demanding cooperation, and they're demanding progress," Obama said after the meeting. "And they'll hold us, and I mean all of us, accountable for it."

The presumed next speaker of the House, John Boehner (R., Ohio), struck a similar note, saying "I am optimistic" about prospects for future cooperation. He said Obama acknowledged that "he hadn't spent as much time with us, reaching out and talking to us, and committed to do so."

Senate Majority Leader Harry Reid (D., Nev.) called it "a very, very efficient, very, very productive meeting."

Republicans insist that their gains on Nov. 2 prove that the public endorsed their view that all Bush-era cuts should be extended, including for the wealthy.

However, a McClatchy-Marist poll taken Nov. 15-18 found a majority, 51 percent, wanting tax cuts extended only for those earning less than $250,000, and 45 percent wanting all the cuts extended.

The poll had a margin of error of plus or minus 3 percentage points.

Neither side has the votes to prevail in the current Congress, where Democrats control both houses but lack the 60 Senate votes needed to cut off debate. If Congress does not act, income-tax rates and taxes on capital gains and dividends will revert to Clinton-era levels beginning Jan. 1.

Tuesday's White House meeting included Geithner; Lew; Vice President Biden; House Speaker Nancy Pelosi (D., Calif.), and Senate Minority Leader Mitch McConnell (R., Ky.).

They agreed that tackling economic issues was their key priority, notably resolving the dispute over the expiring tax cuts and funding the government for the rest of the fiscal year, through Sept. 30, 2011. Without congressional action, government funding will run out Friday. Many Republicans are pushing for a stopgap funding measure that will run out early next year, when a stronger GOP presence in Congress will have a better chance of imposing the kinds of spending cuts the party promised during the campaign.

House Republicans vowed in their "Pledge to America" to roll back spending to 2008-09 levels, saving $100 billion in the first year.

Last year's federal budget deficit was $1.29 trillion, and the nonpartisan Congressional Budget Office projects this year's figure to be $1 trillion.

Republicans will have a strong House majority in the 112th Congress, which begins in early January. Democrats will hold on to a 53-47 majority in the Senate.

Until early January, though, Democrats still control 58 Senate seats and have a 255-179 majority in the House. Their leaders are pushing hard for a budget that makes some trims but will last until the next fiscal year begins on Oct. 1.