WASHINGTON >> Reaching no quick fixes, President Barack Obama and Republican leaders in Congress vowed on Tuesday to seek a compromise on their sharply different views about tax cuts before year’s end.

“The American people did not vote for gridlock,” Obama said following the session. “They did not vote for unyielding partisanship. They’re demanding cooperation and they’re demanding progress and they’ll hold all of us, and I mean all of us, accountable.”

The meeting was the first since the Nov. 2 elections weakened the Democrats’ hold on government, shifting control of the House to the GOP and narrowing the Democratic majority in the Senate. Obama conceded he had not reached out enough to Republicans in the past and promised to consult with them more frequently, GOP lawmakers said.

At one point the president and the lawmakers took the unusual step of leaving their aides behind and retreating the president’s private dining room for a more intimate 35 minutes of discussion.

There was no consensus on whether to keep Bush-era tax cuts in place for the middle class and wealthy alike. But the eight bipartisan congressional leaders and the president agreed to break through their differences by appointing a working group to negotiate a tax cut agreement.

The president appointed Treasury Secretary Timothy Geithner and Budget Director Jacob Lew to the group while party leaders will appoint their own representatives. White House spokesman Robert Gibbs said those negotiations might start later in the day.

Obama said he also emphasized the importance of ratifying a new nuclear treaty with Russia, a treaty that he said has “broad bipartisan support” from national security advisers and secretaries of Defense and State.

“It’s absolutely essential for our national security,” Obama said. “We need to get it done.”

Senate Republican Leader Mitch McConnell said after the meeting that Senate Republicans first wanted to address the expiring tax cuts and pending spending legislation before tackling other issues. Republican Sen. Jon Kyl of Arizona, one of the Republicans who attended Tuesday’s meeting, has rejected the administration’s assertion that the treaty must be dealt with during the lame-duck session, saying the Senate has more pressing issues to deal with.

But Sen. John McCain on Tuesday appeared to leave open the possibility of working with the White House, saying he still hoped progress could be made this year.

“I believe that we could move forward with the START treaty and satisfy Senator Kyl’s concerns and mine about missile defense and others,” McCain said on ABC’s “Good Morning America.”

Sen. George Voinovich, R-Ohio, who earlier this month raised concerns about the treaty’s impact on the former Soviet satellite nations, told reporters, “I’d like to get it done, but in my conscience I want to feel it’s the right thing to do.”

Gibbs, alluding to those comments, said START could still be ratified this year.

The meeting lasted just shy of two hours, nearly an hour longer than originally planned. It was during the last 35 minutes that the president and the lawmakers broke away from their staffs for a more private session.

House Republican leader John Boehner, the Speaker -in-waiting, described the session as a “nice meeting,” but said the hard work of achieving bipartisan agreement still lies ahead.

“The president and Democrat leaders acknowledged that the American people want us to create jobs and to cut spending,” he said.

Obama said that while differences remain over how to address the expiring tax cuts, there was “broad agreement” that both parties can work together to resolve the issue.

“We agreed that there must be some sensible common ground,” Obama said.

The meeting comes as a new Associated Press-CNBC Poll shows most people oppose extending expiring tax cuts for the richest Americans. Just 34 percent want to renew tax cuts for everyone; 50 percent prefer extending the reductions only for those earning under $250,000 a year; and 14 percent want to end them for all.

Obama said he also planned to hold more sessions with lawmakers, a point that Rep. Eric Cantor of Virginia took note of and applauded. “I was encouraged by the president’s remarks regarding his perhaps not having reached out enough to us in — in the last session,” Cantor said, “and that this meeting was the beginning of a series in which he hoped that we could work together in a different fashion for the benefit of the American people, given the problems that we face.”

Obama promised to invite the leaders to Camp David, an offer that he said especially pleased Senate Majority Leader Harry Reid, D-Nev., who pointed out that in his 28 years in Congress he had never been to the presidential retreat in Maryland.

While Obama called the meeting extremely civil, he also spoke of the political realities that often emerge from such meetings — how the leaders of both parties typically fall back on talking points, go before the cameras, try to win the news cycle and paint the other side as unyielding and uncooperative.

“I think there was recognition today that that’s a game we can’t afford. Not in these times,” Obama said. “In a private meeting that I had without staff — without betraying any confidences — I was pleased to see several of my friends in the room say, ‘Let’s try not to duplicate that.’ “

Obama’s work, however, is not limited to building new relationships with Republicans. Democratic allies led by labor decried his federal pay freeze proposal, which would require congressional approval. Moreover, Obama has tried to link arms with Republicans by calling for a moratorium on earmarks, the targeted spending measures that lawmakers insert into legislation. But on Tuesday, most Democrats and a handful of Republicans blocked such an effort in the Senate.