"We are always open to getting involved in races against incumbents. Nobody is entitled to office and primary challenges are a good thing," Senate Conservatives Fund President Matt Hoskins told The Hill in an email. 

"We look forward to getting to know Liz Cheney better and hearing more about her vision for the country. We need new leaders in Washington who will fight against higher taxes and more debt."

Cheney, who announced her bid against Enzi on Tuesday evening, is expected to try to run to his right. But unlike the typical GOP primary challenger, the daughter of former Vice President Dick Cheney has deep connections in Washington, D.C.'s GOP establishment, and won't need the big-hitting Tea Party groups like the Senate Conservatives Fund or the Club for Growth to raise huge sums to spend against Enzi. Still, their stamp of approval could help give her campaign credibility on the right.

A number of issue-based GOP outside groups are taking a wait-and-see approach. Cheney, best known as a foreign policy hawk, has said little about a number of other issues, and while Enzi has been criticized by some on the right for his support of an Internet sales tax law, he has otherwise accumulated a pretty conservative record.

"We are watching the race," was all Club for Growth Spokesman Barney Keller would say at this point.