Enzi has been an extraordinarily conservative senator, in the tradition of the Mountain West. He has a zero percent NARAL rating, a 93 percent lifetime rating from the American Conservative Union and an 86 percent lifetime rating from the Club for Growth.
Enzi's track record alone would make it difficult for anyone to outflank him on the right, let alone build a Senate record that is as or more conservative. But in Cheney's case, despite all her bombast and her famous last name, her previous public positions already show she is less absolutist on social issues than Enzi and no more conservative than him on a range of fiscal and governance issues.
Enzi has strayed occasionally. He angered anti-tax absolutists in his party by supporting parochial legislation to allow states to collect sales taxes for online purchases. And he joined with all but the very most conservative members of the Senate GOP conference to vote for fiscal cliff legislation, which made most of the Bush tax cuts permanent, but allowed them to expire for income above $400,000.
Cheney can attack him from the right on the former, but will eat her own words on the latter. "I think that the potential damage done by going off the fiscal cliff is so significant, that I would hope that even in the town that is very divided right now, people will be able to come together to avoid it," she said on Fox News in November of last year.
Beyond that, though, it's hard to find daylight between the two, except on the issues where Cheney appears to be more liberal.
Enzi voted against both tranches of disaster relief for victims of Hurricane Sandy. He voted against legislation to suspend the debt limit earlier this year.
But he's also voted against social legislation touching on issues where Cheney has staked out fairly liberal views.
He voted against reauthorizing a more expansive Violence Against Women Act, which extended its protections to immigrants, tribal communities, and same sex partners. He voted against repealing Don't Ask, Don't Tell. Recently, as a senior member and former chairman of the Senate Health, Education, Labor and Pensions Committee, he voted against the Employment Non-Discrimination Act, which cleared the panel on a bipartisan basis.
Cheney by contrast has said gay marriage should be left to the states, and that "freedom means freedom for everyone," suggesting she personally supports it. Her views on abortion are unclear.
All of which suggests Republicans in Washington are annoyed by something other than Cheney's hyper-conservatism. It may be loyalty to Enzi. Or the desire to avoid an ugly primary fight involving a candidate with the last name Cheney. Perhaps it's her penchant for engaging in extreme rhetoric.
But though her rhetoric might make her seem farther right than the soft-spoken Enzi, there are decent reasons to think she's actually more liberal than he is.