Corner favorite Jason Chaffetz is mentioned in this Politico story as another solid conservative who is angling for a seat:
Cantor continues to push for reform-minded conservatives on committees such as Appropriations, Energy and Commerce, and Rules — known colloquially as “exclusive committees.” Reps. Jason Chaffetz of Utah and Jeff Flake of Ariz. are the leading conservatives who have shown interest in seats on the spending panel. And in a sign of the shifting dynamics of conservative politics, Boehner and Cantor are signaling that they are unafraid to cross longtime Reps. Jerry Lewis of California and Joe Barton of Texas as they seek to circumvent term limit rules to regain chairmanships.