Representative Jim Jordan was brought down by the revolt of the rule followers.

Withstanding intense pressure, a solid bloc of more mainstream Republicans, many with military and executive experience and a desire to legislate rather than blow things up, pulled the party in their direction. They believed that installing Mr. Jordan, a hard-right Ohioan and political brawler, would reward colleagues who had played dirty in unseating Speaker Kevin McCarthy and undermining the candidacy of Representative Steve Scalise of Louisiana.

It particularly galled them that Mr. Scalise, the No. 2 Republican, defeated Mr. Jordan, the chairman of the Judiciary Committee, in the initial party vote to choose a replacement for Mr. McCarthy only to then watch Mr. Jordan’s allies immediately pivot to denying Mr. Scalise the speakership on the floor. The anti-Jordan lawmakers then found themselves under a withering social media attack from the right and confronting violent threats against them and their families for balking at voting for Mr. Jordan.

It only reinforced the resistance among the Republicans who see themselves as institutionalists. They insist that they just want to legislate in a conservative but orderly fashion and escape the chaos that has rocked Republicans for more than two weeks, damaging their image and their prospects for holding the House in next year’s elections.

“These are the folks who are the ultimate team players,” said Representative Mario Diaz-Balart, Republican of Florida and an informal ringleader of the rule-follower caucus, about those who joined with him and others to beat back the Jordan candidacy. “These are the folks that fall on their swords on tough votes.”