The intraparty race for the chairmanship of the House Republican Conference has intensified in recent weeks, pitting a veteran conservative leader against a rising female star.

Rep. Cathy McMorris RodgersCathy McMorris RodgersLawmakers celebrate 100th anniversary of women getting the right to vote The GOP's commitment to electing talented women can help party retake the House McCain and Dingell: Inspiring a stronger Congress MORE (Wash.), the conference vice chairwoman, is battling Rep. Tom Price (Ga.), who heads the Republican Policy Committee. They are running to replace Rep. Jeb Hensarling (Texas) as the fourth-ranking member of the party leadership; Hensarling is widely expected to become the next chairman of the Financial Services Committee.

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Speaker John BoehnerJohn Andrew BoehnerK Street giants scoop up coveted ex-lawmakers Trump adviser expected to leave White House, join Juul The Hill's 12:30 Report: McGahn inflames Dem divisions on impeachment MORE (Ohio), Majority Leader Eric CantorEric Ivan CantorGOP faces tough battle to become 'party of health care' 737 crisis tests Boeing's clout in Washington House Republicans find silver lining in minority MORE (Va.) and Whip Kevin McCarthy (Calif.) have all privately pledged to remain neutral in the race, lawmakers and aides say, but a loss by McMorris Rodgers could create a political headache, leaving the House GOP leadership without a woman in its upper ranks at a time when Democrats have widened the gender gap at the polls.

Republican leaders have made a concerted effort in recent months to showcase women in the party, frequently including them in weekly press conferences and elevating McMorris Rodgers as a surrogate countering Democratic claims of a GOP “war on women.” The fourth-term Washington state lawmaker is also serving as the House GOP liaison to Mitt Romney’s presidential campaign.

“It’s going really well,” McMorris Rodgers said in an interview. “I’m really encouraged by the support, both among the members around the leadership table, committee chairs, freshmen.”

The conference chairman is a top messaging post for Republicans, and McMorris Rodgers emphasized her work promoting the use of new and social media among members. She said that during her two terms as vice chairwoman, the percentage of members using those tools had grown to 90 percent, from 30.

“I believe that one of my strengths is really bringing people together and leveraging the talent that would be in this conference on the communications front,” she said, “and taking our message to every corner of the country is part of my goal.”

A senior House GOP aide acknowledged the desire among top Republicans to have a woman in a key leadership role. “It’s important,” the aide said.

Yet Price, 57, is equally well-liked by members of the conference, and as a former chairman of the Republican Study Committee he enters the race with deep support among conservatives. He is also an orthopedist who has been a leader in the party on healthcare. 

With the top three GOP leaders all expected to keep their positions, the race for the fourth-ranking leadership post is likely to remain the highest-profile leadership battle. 

McMorris Rodgers and Price used the final few legislative days before members left town to court colleagues aggressively. “They’re both actively working the floor. Actively working,” one House Republican said.

Senior Republicans backing Price’s bid include Hensarling, Ways and Means Committee Chairman Dave Camp (Mich.) and budget chief Paul RyanPaul Davis RyanAmash storm hits Capitol Hill Debate with Donald Trump? Just say no Ex-Trump adviser says GOP needs a better health-care message for 2020 MORE (Wis.), who committed to helping Price before he was picked as Romney’s vice presidential running mate.

“It’s great the conference has two positive choices, but I’m with Tom,” said Rep. Patrick McHenry (N.C.), a member of the Republican whip team. “I’ve seen his leadership on the Republican Study Committee. But Cathy’s done a good job as vice chair. I just think Tom fits the role a little bit better.”

McMorris Rodgers, 43, has locked up support from Rep. Fred Upton (Mich.), chairman of the Energy and Commerce Committee, and Rep. Pete King (N.Y.), chairman of the Homeland Security Committee. Other backers include Rep. Tom Cole (Okla.), a deputy whip, Rep. Jo Ann Emerson (Mo.), and freshman Reps. Tim GriffinJohn (Tim) Timothy GriffinFlynn discloses lobbying that may have helped Turkey Tea Party class reassesses record Huckabee's daughter to run '16 campaign MORE (Ark.) and Renee Ellmers (N.C.).

“I think [McMorris Rodgers] has been a great vice chair and I think she deserves an opportunity to run the conference,” Emerson said. She added that it was “very important” for a woman to keep a seat at the Republican leadership table.

Lawmakers in both camps predicted a close race that could go down to the wire, and while McMorris Rodgers was seen as the early favorite, several Republicans said Price had emerged as the more effective campaigner.

“He’s a very good retail politician,” a House GOP leadership aide said.

One Republican lawmaker said McMorris Rodgers rankled some members by telling them she had the support of party leaders, only to have the leadership insist in private conversations that was not the case. “It could come back to haunt her,” the lawmaker said. “Cathy’s effort has just been a little bit clumsy.”

A spokesman for the congresswoman declined comment, as did representatives for BoehnerJohn Andrew BoehnerK Street giants scoop up coveted ex-lawmakers Trump adviser expected to leave White House, join Juul The Hill's 12:30 Report: McGahn inflames Dem divisions on impeachment MORE, Cantor and McCarthy.

Price declined an interview request. “Right now, what’s most important is talking about our positive solutions and getting our team across the finish line in November,” he said in a statement provided to The Hill. “These types of decisions by the conference are not worked out in the press; they’ll be made after discussions and consultation with members.”

A spokeswoman, Ellen Carmichael, later underscored Price’s point, saying he believed the decision “should be left to the internal deliberations of the members, not played out in the media.”