WASHINGTON — On Tuesday morning, after extended discussions of political fund-raising at the Capitol Hill Club, Speaker John A. Boehner stood to change the subject. He then told his House Republican troops that he would put to a vote a measure to raise the government’s borrowing limit, without preconditions.

After what one member described as “stunned silence,” the speaker quipped, “I’m getting this monkey off your back, and you’re not going to even clap?”

The applause he coaxed was grudging and modest, but most rank-and-file House Republicans understood that their leader was taking the arrows from their right flank that could have been headed for them. By quickly and unilaterally ending the back-and-forth over which amendments to try to attach to a debt ceiling increase, Mr. Boehner avoided another protracted public battle within the party and, more important, steered the government away from a potentially crippling default — without forcing most of his members to vote for a debt ceiling increase.

“We’re not going to make ourselves the story,” he said, according to members in the room.

For the fifth time since January 2013, Mr. Boehner on Tuesday effectively turned the floor of the House over to Democrats to secure must-pass legislation. But rather than weakening his control of the House, he may have strengthened it. He showed a relish for combat, both with the ranks of his right-wing antagonists in the House and with the increasingly angry Tea Party activists off Capitol Hill.