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.