WASHINGTON — Hours after Republicans swept to victory in November 2010, catapulting John A. Boehner to the speaker’s chair, he was asked how he could possibly persuade House conservatives to do some of the tough jobs of governing like raising the federal debt limit.

“We will be working that out over the next couple of months,” a confident Mr. Boehner, of Ohio, said with a shrug.

A canny veteran of many tough Washington negotiations, Mr. Boehner always thought it could be worked out. What he did not count on was commanding a Republican majority with scores of lawmakers who had no interest in working things out but were willing to risk the party’s brand and unleash economic and governmental havoc over policy fights.

Since the first days of his speakership, Mr. Boehner found himself under siege from his right flank for being unwilling to defy President Obama over issues ranging from the debt limit to immigration to Planned Parenthood. After holding off the rebellion for years, a visibly weary, possibly relieved Mr. Boehner surrendered on Friday, stepping aside rather than submitting to an ugly struggle to hold on to power.