WASHINGTON — In the Reading, Ohio, neighborhood where Speaker John A. Boehner grew up, nearly every house had two things on the wall: a crucifix and a photo of the pope. “You never ever expected to meet the pope,” said Jerry Vanden Eynden, a lifelong friend of Mr. Boehner’s. “In all of our minds, the pope was the closest thing to meeting God in person here on earth.”

When Pope Francis comes to Capitol Hill in September, he will be the first pontiff to address a joint meeting of Congress, where more than 30 percent of the members are Catholic. The visit will fulfill a long-held dream of Mr. Boehner, who says only his working-class roots as a bar owner’s son are more essential to his core than his Catholic upbringing. He has extended offers to popes for the last 20 years, and Francis, after taking nearly a year to consider, was the first to accept.

The pope’s visit comes with inherent tension for many Republicans, including those who are Catholic. While he has made no changes in church doctrine, Francis has forcefully staked out ideological ground opposite that of Mr. Boehner and his party. He has excoriated the excesses of capitalism as the “dung of the devil,” pleaded for action to stop global warming and enthusiastically supported the new nuclear accord with Iran.