It seems she's quite serious:
Ms. Cheney, 46, is showing up everywhere in the state, from chicken dinners to cattle growers’ meetings, sometimes with her parents in tow. She has made it clear that she wants to run for the Senate seat now held byMichael B. Enzi, a soft-spoken Republican and onetime fly-fishing partner of her father.
But Ms. Cheney’s move threatens to start a civil war within the state’s Republican establishment, despite the reverence many hold for her family.
Mr. Enzi, 69, says he is not ready to retire, and many Republicans say he has done nothing to deserve being turned out.
It would bring about “the destruction of the Republican Party of Wyoming if she decides to run and he runs, too,” Alan K. Simpson, a former Republican senator from the state, said in an interview last week. “It’s a disaster — a divisive, ugly situation — and all it does is open the door for the Democrats for 20 years.”