LUSK, Wyo. — A young Dick Cheney began his first campaign for the House in this tiny village — population 1,600 — after the state’s sole Congressional seat finally opened up. But nowadays, his daughter Liz does not seem inclined to wait patiently for such an opening.

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 by Michael 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.