Mr. Boehner, a sharp dresser with a two-pack-a-day habit, sometimes gets referred to around Capitol Hill as Don Draper, the character on the television show “Mad Men.” “I’m still who I am. I’m a businessman. I can’t be something I’m not. No apologies. Zero,” Mr. Boehner said in the recent interview, smoothing his hair before heading to a political event…

Mr. Boehner’s opponents, including the president, delight in painting him as a perpetually tan, country-club Republican out of touch with the American people. Mr. Boehner, in response, talks about his father’s work running the family tavern. To put himself through Xavier University in Cincinnati, he says he worked “every rotten job there was and damn glad to have them,” including janitor, roofer and heavy-equipment driver.

His mother “was always pregnant with cloth diapers hanging everywhere to dry,” says Jerry Vanden Eynden, a childhood friend who manages Candle-Lite, a local candlemaker.

Addressing a perennial source of jokes, Mr. Boehner says his dark complexion is natural, similar to that of his mother and four (of 12) siblings. “I have never been in a tanning bed or used a tanning product,” Mr. Boehner said. His staff showed a high-school group photo where he has the darkest face in Moeller High’s all-male class.