By CARL HULSE

The New York Times

September 25, 2015

WASHINGTON — Hours after Republicans swept to victory in November 2010, catapultingJohn 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.

He insisted he could have survived a challenge to his speakership. “I’ve got plenty of people following me,” he said, “but this turmoil that’s been churning now for a couple of months, it’s not good for the members and it’s not good for the institution.”

And with that, Mr. Boehner followed his once-restive wingman, Eric Cantor of Virginia, out the door, a House speaker and House majority leader brought to power by the Tea Party movement, then swept out by the same unquenchable forces.

Despite the criticism from the right of Mr. Boehner as a “squish” or a Republican-in-name only, he was actually a strong conservative with the two-decade voting record and beliefs to match. He was someone who knew how Washington worked and wanted to keep it working as much on Republican terms as possible, given a Democratic president and for a time, a Democratic Senate.

And he succeeded to a significant degree in cutting spending and eliminating the costly earmarks he despised even as he padded the Republican majority through his political savvy and fund-raising prowess.

But Mr. Boehner’s years in Washington and his resistance to putting government through upheaval over unwinnable policy fights were serious sins to conservatives inside and outside the House who have a strong distaste for government and were eager to push their views to the limit. Those same antigovernment conservative influences have had a notable impact on the Republican presidential primary, moving outsiders like Donald J. Trump, Ben Carson and Carly Fiorina to the fore while castigating the Republican establishment in Washington as part of the problem.

The person who replaces Mr. Boehner will face the same situation — a fact that was not lost Friday on House Republicans who seemed to have a bit of a “Now what do we do?” outlook as they absorbed the loss of Mr. Boehner.

Whoever is in the speaker’s chair has the same mathematics,” said Representative Trent Franks, Republican of Arizona.

The next speaker — Representative Kevin McCarthy of California, the current majority leader, is mentioned by many Republicans as the most likely successor — must still find ways to govern in a politically divided city and to appease House conservatives.

Whoever takes over will not find the job any easier. In fact, it could be tougher with emboldened conservatives applying tremendous pressure to confront Democrats and the White House more than Mr. Boehner was willing or able to do. And Mr. Boehner, 65, had the stature, relationships and internal support to resist the rebellion until this point; the incoming speaker will to some degree owe members of the right flank for a job that would not be open were it not for them.

Mr. Boehner’s allies continued to believe he could win a vote on the speaker’s job. But they increasingly heard from supporters of Mr. Boehner that they feared going on the record for Mr. Boehner would attract a primary fight from anti-establishment forces back home. Mr. Boehner acknowledged that one reason for his decision to step aside was to spare his supporters, as well as the institution itself.

“I don’t want my colleagues hurt,” he said. “I don’t want to put my colleagues through all this.”

In the short term, Mr. Boehner’s resignation clears the way to avoid a shutdown next week. With the help of House Democrats, Mr. Boehner no longer has to worry about a challenge to his leadership for doing just that.

Some Republicans said Friday that they should use the month remaining before Mr. Boehner steps aside to deal with the most pressing unresolved problems that so readily annoy conservatives: funding a highway bill, renewing the Export-Import Bank and even increasing the federal debt limit. Mr. Boehner noted that there was a lot of work that needed to be done. “I plan on getting as much of it done as I can before I exit.”

Representative Steve Stivers, Republican of Ohio, said, “This gives us some running room to get things done.”

But Mr. Boehner’s critics will aggressively resist such a strategy. They see his retirement as a capitulation and a recognition that conservative unrest against the establishment — the nexus of K Street and Capitol Hill that Mr. Boehner represented — is taking hold and that the old guard is on the run.

Mr. Boehner is hardly the first House speaker to fall victim to rebellion in the ranks. Democrats lost their control of the House in 1994 after a small group of House conservatives elected a few years earlier began agitating against the leadership with claims that top lawmakers were badly out of touch. Among that group was John A. Boehner.