Oklahoma Republican Reps. Tom ColeThomas (Tom) Jeffrey ColeGOP backs new fund for public health Top GOP rep. calls for probe into abortion services at community health centers Dems push to end ban on gun violence research MORE and James LankfordJames Paul LankfordRepublicans jockey for position on immigration Tillis-Lankford amnesty proposal is a betrayal of the American people This week: Congress gets ball rolling on tax reform MORE could have difficulty picking up conservative support, if they try to replace retiring Sen. Tom CoburnTom Coburn-trillion debt puts US fiscal house on very shaky ground Al Franken: 'I make fun of the people who deserved it' The more complex the tax code, the more the wealthy benefit 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 BridenstineJames (Jim) Frederick BridenstineJim Bridenstine is the leader NASA needs The United States and Canada can make space great again together Trump stacks administration with climate change skeptics 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.