At a closed-door Capitol meeting on Wednesday, Representative Peter Roskam of Illinois was regaling other Republicans with his imitation of Speaker John A. Boehner, imagining him in the current budget negotiations with President Obama. He pretended to drag on a cigarette like the chain-smoking speaker, and blew away smoke and Mr. Obama's tax demands in one raspy retort: "Ain't gonna happen."
Then the actual speaker stepped to the podium to poke fun at the president. "He's chewing Nicorette," Mr. Boehner said to the laughter of the Republicans.
A day later, an Obama adviser was recalling the failed budget talks between the president and Mr. Boehner last year and joked about one tactic for dealing with the speaker, who favors merlot: "Give him a glass of wine, and he'll be better to deal with."
These episodes, while lighthearted, capture the personal gulf between the 51-year-old president and the 63-year-old speaker as they try once again, alone and in private, to negotiate an elusive "grand bargain." The goal is to raise tax revenue and shrink spending to stabilize the national debt and, more immediately, prevent a fiscal crisis come January, when more than $500 billion in tax increases and across-the-board spending cuts are to take effect absent a deal.
But it is a negotiation between two men who have little regard for the other's bargaining skills, with a relationship soured by the mutual recriminations after their failure 18 months ago, people on both sides say.
An Oval Office meeting last Sunday was their first one alone since that time. They met again on Thursday night and spoke by phone on Friday. People familiar with the talks said Mr. Boehner offered to allow tax rates to rise for income above $1 million; Mr. Obama is holding out for the $250,000 threshold, but administration officials considered the Boehner overture a sign of progress.
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With little in common, Mr. Boehner and Mr. Obama never have had more than a distant, respectful relationship. Both avid golfers, they have played together just once, an outing in June 2011 that led to their first attempt at a budget deal.
Mr. Boehner has told friends, "We just don't speak the same language." Mr. Obama told the author Bob Woodward that if the speaker "had more control of his caucus," they would have sealed the deal last year. Referring to two past Republican leaders, Mr. Obama added: "I could have done a deal with Bob Dole. I could have even done a deal with Newt Gingrich."
Past and current Obama administration officials say Mr. Boehner has little grasp of strategy and less of a hold on policy details. Yet Mr. Boehner is confident that he is the one with depth and experience in deal-making and regards Mr. Obama as a naf.
A Republican aide familiar with the talks said the president had spent long stretches trying to persuade Mr. Boehner of the wisdom of his positions, which the speaker views as "an enormous waste of time," the aide said. Conversations in the past few days have been 90 percent Mr. Obama, 10 percent Mr. Boehner, the aide said.
Aside from their divergent views of their abilities, the two men's goals are at cross-purposes. Mr. Obama vows to end the Bush-era tax cuts for high incomes so that the wealthy contribute toward deficit reduction that would otherwise fall on the poor and middle class. Mr. Boehner says he is willing to increase revenue somehow but not by raising tax rates — though to do even that, he needs to show his fellow Republicans a presidential commitment to significantly more savings from entitlement spending, chiefly Medicare, than Mr. Obama has proposed.
Last year, Mr. Boehner had the edge as Mr. Obama faced a difficult re-election campaign and needed Republicans' support to increase the nation's borrowing limit, lest the government default. Now, after a decisive re-election victory and Democratic gains in Congress, Mr. Obama has the stronger hand. He also made higher taxes for the wealthy a central campaign issue, suggesting a mandate borne out in public polls. And he benefits from a hard deadline, Dec. 31, after which all of the Bush-era tax cuts expire if action is not taken to extend them. Polls show that voters would hold Republicans responsible if no deal is reached in time.
Unlike last year, when Mr. Obama and Mr. Boehner negotiated while looking toward the 2012 elections, they now meet knowing that in all likelihood they will be dealing with each other for the foreseeable future and that their legacies and the good of the country depend on constructive engagement.
"Neither one can afford to win an absolute victory over the other," said one Republican lawmaker who is close to the speaker but did not want to be identified commenting on the delicate talks. "If you push him into a deal that costs him his speakership, the next guy up is not going to be to the left of John Boehner. And we don't want a weak president."
The men's relationship did not start badly. Mr. Obama has said that Mr. Boehner reminded him of the Midwestern "Rotary Club Republicans" he worked with in the Illinois Senate. Aides say Mr. Obama especially appreciated Mr. Boehner's geniality, given what administration officials see as the contemptuousness of the Senate Republican leader, Mitch McConnell of Kentucky.
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"I think in '11 they had a pretty good relationship," said William M. Daley, Mr. Obama's chief of staff at the time. "The president always thought: 'I know this guy. I used to work with people like that in the legislature in Springfield — kind of a moderate Republican, suburbanite. And I can deal with this guy.' "
"Things are very different now with the re-elected President Obama and the way he relates to Republicans," Mr. Daley added.
Mr. Obama spent his first two years with large Democratic majorities in the House and the Senate, which obviated much need for bipartisan negotiations. Then Republicans seized control of the House in the 2010 midterm elections; a humbled president was immediately forced into a series of fiscal negotiations with the empowered opposition.
The results were one-sided: Republicans won a two-year extension of all Bush tax cuts and lower estate taxes, as well as $1.4 trillion in spending cuts and not a penny in higher taxes. That left many Democrats grousing that Mr. Obama was getting snookered, and convinced Republicans that their leaders could always out-negotiate the president.
"The president has enjoyed legislative success when he's had open-field running," Mr. Roskam said, referring to the years when his party controlled the White House, the Senate and the House. "But in terms of divided government, he's not the person who seems to be able to put the deal together."
Yet Mr. Obama won some concessions, including temporary payroll tax cuts and terms in last summer's debt limit compromise that gave him another advantage in these talks. That compromise required the deep across-the-board cuts that will take effect in January if the parties do not reach an agreement, and those cuts fall harder on military spending while exempting Medicaid — giving Republicans arguably more cause to try to avoid their taking effect.
Republicans acknowledge that Mr. Boehner has the weaker hand, but they say he has the stronger skills, having participated in difficult negotiations dating to his days as a committee chairman, including against Senator Max Baucus of Montana, the chairman of the Senate Finance Committee, and Senator Edward M. Kennedy.
Shortly before Mr. Kennedy died, a teary Mr. Boehner told how he had once been alone in his House office late one night, with talks on an education bill bogged down, and looked up to see a grinning Mr. Kennedy in the doorway. Rarely do senators cross over to the House for legislative chitchat, let alone one so famous and senior.
Mr. Obama's critics say he would have been wiser to court Mr. Boehner in a similar fashion. But the president's supporters say he is constrained by Republicans' sense of political risk if they are seen as too close to him.
"It's a myth that the president didn't reach out to Congress," said Phil Schiliro, formerly Mr. Obama's chief liaison to Congress. "But socializing with the president doesn't always make it easier for Speaker Boehner or other Republican leaders to get their caucuses to come along."
However the budget talks end, the Obama-Boehner relationship has broken into pop culture. "Saturday Night Live" recently portrayed a joint news conference in which the self-confident president announced a deal.
"I had the leverage — why give in?" said the president, played by Jay Pharoah. "Well, simply put, I felt sorry for this man. I realized how badly the Republican Party treats him when he even considers raising taxes."
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