A quartet of House Republicans eyeing Senate runs were among the 66 Republicans who voted against the bipartisan compromise to increase the debt limit. GOP Reps. Todd Akin (Mo.), Jason ChaffetzJason ChaffetzSenate passes dozens of bills on way out of town Oversight panel demands answers on Pentagon waste report Chaffetz: Congress will ‘absolutely’ look at 5B in waste at Pentagon MORE (Utah), Denny Rehberg (Mont.) and Jeff FlakeJeff FlakeSenators move to protect 'Dreamers' Reid bids farewell to the Senate Reid defends relationship with McConnell in farewell speech MORE (Ariz.) all broke with their party's leadership and opposed the agreement.

Akin is in a contested primary against former Missouri State Treasurer Sarah Steelman, with businessman and longtime Akin donor John Brunner seriously looking into joining the race. Steelman came out in support of an earlier Republican bill that included a balanced-budget amendment. The eventual Republican nominee will face off against Sen. Claire McCaskillClaire McCaskillSunday shows preview: Trump sits down with Fox Democrats unnerved by Trump's reliance on generals Senate passes stopgap funding bill, averting shutdown MORE (D-Mo.), who said Monday that while the bill was not perfect, she was "ecstatic about compromise" and that House members would have to "lose their minds" to not pass the bill.

Chaffetz is considering a challenge of longtime Republican Sen. Orrin HatchOrrin HatchTax reform: Starting place for jobs, growth Overnight Finance: Senate Dems dig in as shutdown looms | Trump taps fast-food exec for Labor chief | Portland's new CEO tax Mnuchin, Price meet with GOP senators MORE (Utah), who has said he is unlikely to vote for the deal in the Senate Tuesday. He has been trying to shore up his conservative bona fides since it became clear he could face a challenge from the right, although Chris Chocola, president of the conservative Club for Growth, indicated to The Hill Monday that Hatch's recent votes won't stop the deep-pocketed group from targeting him.

Rehberg is running against Sen. John Tester (D-Mont.), and Flake is running for the Arizona Senate seat that will be vacated by retiring Sen. John Kyl (R).

Chaffetz and Akin are dependent on their state's Tea Party adherents to win their primaries. Flake is unlikely to face a serious primary, but has taken some centrist stances on immigration that have angered some of the state's conservatives.

Rehberg will likely have a clean shot at Tester in the Republican-leaning state. He said he could not support the plan because it did not include a balanced-budget amendment.