By Scott Wong and Cristina Marcos - 03/12/15 06:00 AM EDT

When House Administration Committee Chairwoman Candice Miller retires and hands over her gavel next year, GOP leaders will be facing a familiar quandary: finding another female lawmaker to lead a committee.

Miller, a Michigan Republican, is the only woman among the 21 GOP committee chairs. And leadership — cognizant of the poor optics of a potential all-white, male lineup — will be scrambling to replace her.

“If we don’t have a woman chairman, that will be a big problem,” said a former GOP leadership aide.

Math is the biggest barrier to more women leading congressional panels. Of the 88 women serving in the House, including delegates, only 23 are Republicans. And just eight of them served in Congress before 2011.

That simply leaves the GOP with fewer women to elevate, particularly given that seniority plays such an important factor in determining who gets a gavel.

The male-female ratio isn’t that much better in the upper chamber, which is also controlled by Republicans. Of the 20 Senate committees, women chair just two. Sen. Lisa Murkowski (R-Alaska) leads the influential Energy and Natural Resources Committee, while Sen. Susan Collins (R-Maine) heads the Select Committee on Aging.

House Republicans are doing better when it comes to their leadership team, with three women serving in lower-profile leadership posts. As conference chairwoman, Rep. Cathy McMorris Rodgers (Wash.) is the No. 4 House Republican. Rep. Lynn Jenkins (Kan.) is the conference’s vice chairwoman, and Rep. Virginia Foxx (N.C.) is the conference secretary.

The party also added nine women to its ranks during the past two election cycles, something party leaders hope translates into more women holding gavels down the road.

“Nearly half of the House Republican leadership team is women. Obviously, it would be great if more committee chairs were in the future,” said Michael Steel, a spokesman for Speaker John Boehner (R-Ohio).

By comparison, there were four committee chairwomen during former Speaker Nancy Pelosi’s first term, the California Democrat’s office said. Today, eight Democratic ranking committee members are women, and 13 are either a woman or person of color.

The next Congress’s Speaker could easily replace Miller with another woman because the Administration slot is selected by the Speaker. But chairing the low-profile panel, which runs day-to-day operations of the House, isn’t exactly a powerful or coveted job.

The Speaker also handpicks the chairmen of the Rules, Ethics and Intelligence committees, so those could be opportunities as well. Republicans, however, may want some continuity at those panels: Rep. Pete Sessions (Texas) took over Rules in 2013, while Reps. Charlie Dent (Pa.) and Devin Nunes (Calif.) are brand-new chairmen at the Ethics and Intelligence panels, respectfully.

Chairmen of other prized committees — including Appropriations, Armed Services, Judiciary and Ways and Means — are chosen by the Steering Committee, which is largely made up of Boehner, Majority Leader Kevin McCarthy (R-Calif.), Majority Whip Steve Scalise (R-La.) and their allies. The 28-member panel relies on seniority, but it doesn’t always pick the most senior member of a particular panel.

Here’s the shortlist of Republican women who could win a gavel in the 115th Congress:

• Rep. Ileana Ros-Lehtinen (Fla.) is the most senior female House Republican and the fifth most senior among all House women, arriving on Capitol Hill in 1989. But the Cuban-American already had a turn as chairwoman of the House Foreign Affairs Committee in the 112th Congress.

• Rep. Kay Granger (Texas) is a senior appropriator who chairs the House Appropriations subcommittee overseeing the State Department and foreign aid. She also led a working group to address the influx of child migrants crossing the southern border last summer.

Granger is known for her close attention to detail, reviewing appropriations measures from her subcommittee line by line. She isn’t overtly partisan and is respected by members on both sides of the aisle.

It’s possible she could leapfrog two other male colleagues on the committee to succeed Appropriations Committee Chairman Hal Rogers (R-Ky.), who is term limited in 2016. But she would need the backing of the Steering Committee.

• Foxx could seek the gavel of the Education and the Workforce Committee, which Chairman John Kline (R-Minn.) will have to relinquish next year due to term limits. But Foxx would have to beat out a more senior colleague: conservative Rep. Joe Wilson (R-S.C.).

• Rep. Marsha Blackburn (Tenn.) is vice chairwomen of the influential House Energy and Commerce Committee.

Term limits will force incumbent Chairman Fred Upton (R-Mich.) to give up his gavel in 2016, which could give an opportunity to Blackburn.

Leadership has frequently employed Blackburn to handle important initiatives. In 2013, she managed the floor debate on a controversial anti-
 abortion-rights bill after the measure’s sponsor, Rep. Trent Franks (R-Ariz.), created a firestorm by suggesting rape rarely causes pregnancies.

The Tennessee Republican, who has served in the House since 2003, frequently appears on cable TV and is polished and telegenic.

Seven other male lawmakers rank higher in seniority than Blackburn on Energy and Commerce, but it wouldn’t be entirely unprecedented for her to leapfrog them.

• Rep. Cynthia Lummis (Wyo.) serves on the Oversight and Natural Resources Committees and chairs the Oversight subcommittee on the interior.

But both the Oversight and Natural Resources committees have new chairmen who just took over in January. And GOP sources said she may be a bit too conservative for Boehner or the Steering panel to give her a gavel.

Miller, a former Michigan secretary of State who’s served in Congress since 2003, declined to comment on the need for more chairwomen. But in an email to The Hill, McMorris Rodgers praised Miller as an “exemplary leader” in the House.

“While we will certainly miss Candice’s leadership on the House Administration Committee, I have no doubt that her service will encourage more women to seek chairmanships in the future,” McMorris Rodgers said.

“House Republicans are proud to have half of our elected leadership positions filled by women,” she said, “and we’re looking forward to watching that number grow in the next Congress and beyond.”