Boehner helped fill out that portrait as he described the scene at one of their negotiating sessions.
"All you need to know about the differences between the president and myself is that I'm sitting there smoking a cigarette, drinking merlot, and I look across the table and here is the president of the United States drinking iced tea and chomping on Nicorette," he told Woodward.
Beyond golf, the two "really don't have a whole lot in common," says Rep. Steve LaTourette of Ohio, a friend of the speaker.
"Boehner loves to tell stories about growing up in a bar," says LaTourette. "He really is a self-made guy, and the president is a professor. And that's a little bit like oil and water in terms of being best buds. But they don't have to be best buds."
LaTourette says Boehner has been managing the pressure with his trademark even temperament.
"He still gets out and gets his exercise; he'll still like to get a glass of wine in the evening," says LaTourette. "If he's all tied up in knots and tense, it has to be way deep inside him because you don't see it on the surface. It's true, he doesn't even cry as much anymore."
Boehner has taken a ribbing for years about his penchant for choking up over big moments, little kids and just about anything in between.
In return, the smartly dressed speaker likes to tease colleagues and reporters alike about their sartorial shortcomings.
"Tie's a little long today, isn't it?" he deadpanned to one reporter as he walked through the Capitol on Wednesday.
Terry Holt, a former Boehner aide who remains close to the speaker, said Boehner leads a conservative caucus, "but it's one that has learned a thing or two since he became speaker. They've matured — and Boehner has matured along with them."
For one thing, Boehner has taken pains to present a more unified front with his fellow House GOP leaders in the current debt talks, after constant speculation over the previous two years that ambitious underlings were angling to replace him. A recent letter to Obama that signaled a willingness to raise more revenue as part of the budget deal was notably also signed by six other House GOP leaders.
A favorite maxim that Boehner likes to recite helps to capture the speaker's approach, and his challenge: "A leader without followers is just a man out for a walk."
Boehner, who lives in a basement apartment in Washington while his wife stays in Ohio, is putting in longer hours these days but still keeps largely to his usual routine. He's up early to check news sites and perhaps get in a walk before breakfast at a diner, then on to Capitol Hill by 9 a.m. He's typically in bed by 10 p.m.
He doesn't hang out in the lobby off the House floor, smoking and kibitzing as he did before becoming speaker.
"The quality of life is not like it was before he was speaker," says Rep. Pat Tiberi of Ohio, a longtime friend of the speaker. "He doesn't play golf as much. He travels and helps members. I wouldn't say it's a very fun job."
Boehner still shows flashes of his dry humor, though.
He drew laughs for dishing off a rhyming dodge to reporters Thursday when asked if he would allow separate votes on middle-income tax rates and rates for the wealthy
"Ifs, ands and buts are like candy and nuts," he said. "If that's the case, every day would be Christmas."
Presiding over the lighting of the Capitol Christmas tree, Boehner took time to fuss over the optics of his photo op with a Colorado high school student invited to turn on the lights.
"Now here, button your coat, button your coat, c'mon," he gently admonished Ryan Shuster of Colorado Springs. "Ryan, pictures last forever, OK?"
The speaker, who ran a plastics and packaging business before his life in politics, is known for his down-to-earth descriptions of the dynamics on Capitol Hill.
Speaking about the difficulties of leading his diverse caucus, he once explained: "It's hard to keep 218 frogs in a wheelbarrow long enough to get a bill passed," referring to the number of votes needed to approve legislation.