WASHINGTON — Republicans expanded their numbers in the House and won the Senate in 2014 by asking voters to give them control of Congress and let them prove they could govern the country. Right now, they appear unable to govern themselves.

Representative Kevin McCarthy’s abrupt withdrawal Thursday from a speaker’s race he had been favored to win threw the House into tumult and left open the question of who would lead the chamber as Congress faces a series of deadlines to fund the government and keep the nation’s credit intact. It also threatened the party’s credibility with a presidential election just a year away.

The chaos was the latest illustration that hard-right, Tea Party-influenced conservatives who have broken from the Republican establishment have made good on their promise to upend the traditional order in Washington. Other Republicans, blindsided, were assessing their options Thursday, even as Speaker John A. Boehner sought to calm nerves by saying that he would stay on the job until a replacement was found.

Just as they had celebrated Mr. Boehner’s decision last month to offer himself as a sacrifice to keep the government operating via a short-term funding bill, conservative activists cheered Mr. McCarthy’s decision, despite the uncertainty it sowed throughout the capital.