WASHINGTON — Stinging from double-digit election losses among female voters, House Republicans elected a woman to their top leadership team Wednesday in a tense test of gender politics and the clout of the GOP’s power brokers.

The election of Rep. Cathy McMorris Rodgers of Washington state to the No. 4 leadership position among House Republicans dispatches conservative favorite Tom Price of Georgia, who had been endorsed by Mitt Romney’s running mate, Rep. Paul Ryan of Wisconsin. House Speaker John Boehner didn’t take sides, but McMorris Rodgers was considered the leadership favorite.

Newly elected Rep. Susan Brooks of Indiana said it was important to have a woman in a top role.

“It does show our party values strong female leadership,” Brooks said of McMorris Rodgers’ election. She said she expects the party now to “try and do a better job of getting our message out to a broader audience.”

The race for such an obscure post carried big symbolism after women voted for Democrats by an 11-point margin in the presidential and generic congressional races, according to an exit poll by The Associated Press and television networks. Republicans widely decried their party’s domination by white males, and Democrats declared themselves the party of diversity.

In the Senate, the GOP was once thought to be poised to gain control of the chamber but instead lost two seats to Democrats. In the House, Republicans retained the majority but lost as many as eight seats, with some races still uncalled. And Obama defeated Romney 332-206 in the Electoral College.

The lessons of the election weighed heavily on the lawmakers returning this week to Capitol Hill for a lame-duck, end-of-year session. McMorris Rodgers’ supporters had touted her conservatism and her work as Romney’s House liaison. Ryan touted Price as a proven leader and advocate of conservative policies on budget, tax and health care issues. Vote totals were not released.

Earlier in the day, House Minority Leader Nancy Pelosi, D-Calif., surrounded herself with other female lawmakers to announce that she will run again for leader despite her party’s failure to gain the 25 seats it needed to flip control of the House. The nation’s first female speaker of the House, Pelosi largely skipped over that disappointment and focused on election results that she said made her caucus the most diverse in history.

“The point is that if America is going to reach its full fulfillment as a nation, we must have the further empowerment of women,” said Pelosi, who put the formality of leadership elections off until after Thanksgiving.

Her motivation was closer to home, too.

“Being actively involved in politics at this level is really insatiable,” Pelosi said. “There’s so much more I want to do, I don’t know how to get any more hours in the day. You can only sleep so less.”

House Republicans reacted with derision.

“There is no better person to preside over the most liberal House Democratic caucus in history than the woman who is solely responsible for relegating it to a prolonged minority status,” said Paul Lindsay, spokesman for the National Republican Campaign Committee. “This decision signals that House Democrats have absolutely no interest in regaining the trust and confidence of the American people who took the speaker’s gavel away from Nancy Pelosi in the first place.”

Pelosi’s announcement was one of several throughout the day that would give more clarity to the leadership and direction of the next Congress. As in the House, senators re-elected their top leaders, Nevada Democrat Harry Reid and Kentucky Republican Mitch McConnell. Republicans elected Texas Sen. John Cornyn as the vote-wrangling whip, South Dakota Sen. John Thune as the GOP conference chairman, Wyoming Sen. John Barrasso as policy committee chairman and Kansas Sen. Jerry Moran as chairman of the National Republican Senatorial Committee, the party’s campaign arm.

For Senate Democrats, Illinois Sen. Dick Durbin remains whip and New York Sen. Chuck Schumer of New York remains policy committee chairman. Washington Sen. Patty Murray will serve as secretary, leaving open the chairmanship of the Democrats’ campaign committee. Colorado Sen. Michael Bennet was said by Democratic officials to be a leading contender for that spot.

Another question answered about the makeup of the next Congress: Newly elected Sen. Angus King, a Maine independent, announced that he will caucus with Democrats next year.