WASHINGTON — The central conflict that has dogged Speaker John A. Boehner is this: how to answer the hue and cry of the far-right corner of his conference — especially the most conservative of the 87 freshmen who often seem willing to walk to the point of legislative disaster over a point of principle — and actually get things done.

Mr. Boehner finally chose to slam the door on his highly opinionated conference on Thursday afternoon, telling lawmakers that their view on the extension of the payroll tax break was no longer of interest. He was, he said, ready to accept the Senate’s short-term solution, which passed both chambers and was signed by President Obama on Friday.

When Congress reconvenes next month at the start of what inevitably will be a highly contentious election year, Mr. Boehner will find out whether his less-experienced members have finally been schooled in the way of divided government or if they will dig in against him, posing a potential threat to his leadership.

“I’m disappointed in our entire leadership team,” Representative Tim Huelskamp of Kansas said in an interview Friday with CNN, adding that he had considered returning to the Capitol to protest the vote. “After one year watching what’s occurred and seeing our conservative principles falling by the wayside numerous times in these debates, we’ve got a lot of progress to make.”