House Budget Committee Chairwoman Diane Black Diane Lynn BlackBottom line Overnight Health Care: Anti-abortion Democrats take heat from party | More states sue Purdue over opioid epidemic | 1 in 4 in poll say high costs led them to skip medical care Lamar Alexander's exit marks end of an era in evolving Tennessee MORE (R-Tenn.) is intent on maintaining her chairmanship despite announcing plans Wednesday to run for governor in her home state.

“She will remain chairman for the time being and is focused on getting this budget across the finish line,” a spokesman for Black said.

But a 2014 GOP rule named for House Speaker Paul Ryan Paul Davis RyanKenosha will be a good bellwether in 2020 At indoor rally, Pence says election runs through Wisconsin Juan Williams: Breaking down the debates MORE (R-Wis.) would prohibit Black from staying in the position while running for outside office unless she obtains a waiver.

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Black ushered the House Budget resolution through the committee, but so far has not garnered enough support to pass it on the House floor.

It is unclear exactly when she would be required to give up her gavel. The House is in recess until September, and the Republican Steering Committee, which makes the call on waivers and new chairmen, will also be out until then.

Other committee members are already eyeing the position, with Rep. Bill Johnson William (Bill) Leslie JohnsonPG&E pleads guilty to 84 felony counts of involuntary manslaughter in 2018 Camp Fire The Hill's Campaign Report: Republicans go on the hunt for new convention site Police unions coalition director: Biden 'off the deep end' in calls for reform MORE (R-Ohio) seeking to take over.

Another committee member, House Freedom Caucus member Rep. Dave Brat (R-Va.), also floated the possibility of getting the gavel.

"If my colleagues think having a Ph.D. in economics on the budget would be good for our country, I would be happy to serve," he said.

— Scott Wong contributed to this report.