Oklahoma Republican Reps. Tom Cole and James Lankford could have difficulty picking up conservative support, if they try to replace retiring Sen. Tom CoburnTom CoburnAl Franken: 'I make fun of the people who deserved it' The more complex the tax code, the more the wealthy benefit Congress, stop using our nation's military policy for political purposes MORE (R-Okla.). 

Coburn's retirement is likely to set off a GOP primary scramble to fill the seat following the conservative favorite's Thursday evening announcement he will leave two years early at the end of this year ... Oklahoma Gov. Mary Fallin (R) announced Friday the special election to replace him will be held on the same day as this year's regular elections.

In an email to The Hill, Club for Growth spokesman Barney Keller suggested the group would have trouble backing both of the congressmen in a primary.

“We do not know who will run for Sen. Coburn’s seat, but we do know that Sen. Coburn has an outstanding 96 percent lifetime score on the Club for Growth’s congressional scorecard and is a champion of economic freedom. On the other hand, Congressman Lankford has a lifetime 78 percent and Congressman Cole has a lifetime 73 percent, both of which are obviously substantially different from a score in the 90s," he noted.

"We’d love to be able to support a candidate that would mirror Sen. Coburn’s pro-taxpayer record," Keller added.

The Club's opposition to the two comes as little surprise — Cole has sparked the ire of conservatives for his willingness to compromise with Democrats, and the Club backed Lankford's primary opponent in 2010 — but it underscores an opening in the primary for a candidate to take up the conservative mantle.

Both men either are or have been in House leadership, Cole is a former chairman of the National Republican Congressional Committee and a close ally of Speaker John Boehner (R-Ohio), while Lankford is chairman of the Republican Policy Committee. 

Rep. Jim BridenstineJim BridenstineHouse lawmakers back amendment requiring Pentagon climate change report Lawmakers sound alarm on space security The Hill's Whip List: 36 GOP no votes on ObamaCare repeal plan MORE (R-Okla.), who is also a potential contender for the seat, could be the conservative pick. He was endorsed by Senate Conservatives Fund — their only House endorsement — and since casting one of his first votes to oust Boehner, has been an outspoken proponent of conservative causes.

Bridenstine upset Rep. John Sullivan in the 2012 primary, but he hasn't been in Congress long enough yet to have a cumulative voting score from conservative groups.