Having lived in WY for several years, I believe that for Cheney, Wyoming seems like a business arrangement. She owns a mansion in Jackson Hole (WY is a nice tax shelter for the uber-rich), in which she spends the minimum time necessary in order to qualify for "state residency". She also has far deeper pockets than her competition.
That said, she has made a few statements in the past that I agree with. However, I don't believe she operates with her constituent's best interest at heart (but then, who does?).
Bearing in mind that a large chunk of WY is so libertarian that they are at odds with Republican policy anyway... which is part of the reason I felt so at home there. Lol...