Representative Cathy McMorris Rodgers, a Republican from Washington (Andrew Harrer — Bloomberg).

House Republicans chose Washington Rep. Cathy McMorris Rodgers as House committee chairman Wednesday, settling a contest for the GOP’s fourth-ranking leader that had taken on outsized importance as a test for conservatives pushing for greater roles in House leadership.

Though Boehner was publicly neutral in the race, the GOP establishment was known to favor McMorris Rodgers, who enjoyed the support of seven committee chairman and has been a loyal lieutenant to House leaders. She had faced Georgia Rep. Tom Price for the job.

She served as Republican presidential candidate Mitt Romney’s liaison to the House Republicans. Had she lost, the House GOP’s top leadership positions would all have been held by men, at a time when the party’s lack of diversity has become electorally problematic.

But many conservatives, who have at times been skeptical of Boehner’s leadership, preferred Price, whose bid received a push this week after vice presidential candidate Rep. Paul Ryan endorsed him for the job, despite McMorris-Rodgers’s assistance during the campaign.

McMorris Rodgers will replace Rep. Jeb Hensarling (R-Tex.), current GOP conference chairman, who is expected to step down from the job to become chairman of the Financial Services Committee.

The vote came in a closed door organizing meeting of House Republicans where they confirmed that Boehner will continue serving as speaker in the next Congress. Rep. Eric Cantor (R-Va.) was also reelected as Majority Leader and Rep. Kevin McCarthy (R-Calif) as the conference’s whip.

Republicans are still grappling with their role in a Washington next year that will include an enlarged Democratic majority in the Senate and a reelected President Obama.

In a closed door meeting Tuesday morning, Boehner counseled fellow members that the party needs to remain unified as negotiations heat up in coming weeks over how to avoid the so-called fiscal cliff, when a series of tax hikes and spending cuts are set to take place. But he also suggested the group would need to be patient, telling them he made his position clear to the White House last week when he advocated a deficit reduction deal that would include new revenues from reforming the tax code along with cuts to entitlements.

He said he now awaited a counter offer from President Obama, who has called Congressional leaders to the White House on Friday. He said he expected no dramatic action in the talks until sometime after Thanksgiving.