Let's be honest here: Liz Cheney really doesn't want to be a U.S. Senator, she wants to be president. Thus she's got to have experience in elected office, and the Senate would give her a credible, if not esteemed, perch to launch a presidential bid.
As for the politics of Wyoming, they say Mike Enzi's well liked, although no doubt tea party conservatives could pick through his voting record and find thing to grumble about. Is Liz Cheney that grassroots as to have automatic support of the conservative outsiders storming the gates of Washington? I don't know, although certainly anti-incumbency sentiment could help her in the primary.
Personally, I'd like to see a President Cheney, hence I fully support her upstart challenge to the incumbent. But the whiff of carpetbagging is strong, and lots of establishment types --- D.C. beltway hacks who have a lot of power --- aren't so thrilled with Cheney's chutzpah, so we'll see.
At the Hill, "Liz Cheney to primary Sen. Enzi in Wyoming." (Via Memeorandum.)
PREVIOUSLY: "Liz Cheney Looking to Challenge Mike Enzi for Wyoming Senate."