They have a neo-Nazi running in the Republican primary.
Not just a neo-nazi.. a mercenary neo-nazi!
http://thepoliticalcarnival.net/2013/06/28/first-looney-toon-declares-for-14-meet-former-soldier-of-fortune-thomas-bleming/On a serious note, yes most WY GOP elected officials in state dislike Cheney, and dislike her running, and will stick with Enzi. Lummis especially is going to be tenacious for him, because she wants his seat next time, and Cheney could take that away from her.
Neo-Con and Bush money may pour into Cheney though, and people like Erickson do have impact.
In such a small state with tiny media markets that are cheap, things are going to get oversaturated incredibly fast, and every voter in the state could more or less be personally spoken to by the campaigns, so expect a lot of bad blood, also it is a close knit state.
In the end though I think Cheney is too much of a carpetbagger to win, and the Rand Paul faction of the GOP will fight hard against her.. given Ron Paul got 20% of the caucus vote in the 2012 GOP caucus there, that is a sizable faction.