"If he doesn't get a waiver, I would certainly consider the chairmanship of the committee," she said.
Several other men are running unopposed. Reps. Mac Thornberry and Mike Conaway, both of Texas, are presumed to head the Armed Services and Agriculture committees, respectively. There are races for both the Ways and Means and the Oversight and Government Reform committees, yet in both cases, all the candidates are white men. (Rep. Paul Ryan is expected to take the Ways and Means gavel while Rep. Jason Chaffetz appears to be the front-runner for the Oversight panel chairmanship, though the four-way race is tight.)
Meanwhile, white men are also expected to head lower-wattage committees, such as Natural Resources and Small Business, where the gavels look to be held by Reps. Rob Bishop and Steve Chabot, respectively. Staff for Rep. Jaime Herrera Beutler, the only woman on the Small Business panel, confirmed that she is not running, while Rep. Cynthia Lummis, the only woman on Natural Resources, is running to be chair of the Republican Study Committee, a caucus of conservative members. That race also looks likely to be won by a white man, Rep. Mick Mulvaney.
Beside the House Administration Committee, Boehner has sole authority to appoint the chairmen of four other committees, and if Boehner wants to make a dent in the demographics, he could appoint a woman to chair the Ethics Committee, largely viewed as a thankless job whose duties consist of investigating colleagues. Rep. Susan Brooks is the only woman on that panel and is its least senior member.
Boehner also controls the appointment of the Budget Committee chairmanship, but it is widely believed Rep. Tom Price, the vice chairman of the committee, will assume that role. Staff for Rep. Diane Black, the highest-ranking woman on the panel, confirmed she is not seeking the gavel.
In addition, Boehner appoints the Rules Committee chairman, and Foxx is vice chairwoman, but Rep. Pete Sessions is unlikely to be replaced. The Intelligence Committee chairmanship is also speaker-appointed, and Rep. Devin Nunes is said to be the top candidates. Nunes, a Hispanic of Portuguese descent, would be the GOP's sole racial minority in a chairmanship.
In recent years, House Republicans have addressed their demographic problems and elected three women into leadership. In addition to Foxx's role, Rep. Cathy McMorris Rodgers is the conference chairwoman and Rep. Lynn Jenkins its vice chairwoman. Several women also hold subcommittee chairmanships across the conference.
Before Miller became a committee chairwoman, Rep. Ileana Ros-Lehtinen, the most senior female Republican in the House, headed the Foreign Affairs Committee, but she was term-limited. When Ros-Lehtinen, who is Hispanic, stepped down from the chairmanship, the GOP also lost its only racial minority atop any committee. By contrast, seven black or Latino members are the top Democrat on committees, a number that will likely rise next year due to the retirements of white men who will be replaced by women or minorities.
CORRECTION: A previous version of this story incorrectly stated that Rep. Candice Miller's office did not respond to an interview request. The story also incorrectly described her record of committee service: Miller served on the House Administration Committee during the 108th Congress.