Cheney Family Values

The benefits and burdens of running on a famous name

Marc Piscotty / Getty Images

Liz Cheney, the daughter of former Vice President Dick Cheney waits in the hallway for a news conference to begin at the Little America Hotel and Resort in Cheyenne, Wyoming.

Inside a Cozy Wyoming living room, Liz Cheney is putting family first. The Republican Senate hopeful opens a pitch to a wine-sipping crowd with a tale about the time her daughter Grace, now 13, heard Barack Obama say he wanted to bring accused terrorists to the U.S. for trial. "Use your brain, dude," the girl chirped at the TV, according to her mom's retelling. "That's totally stupid." The room burst into applause.

An admirable closeness has long been the defining feature of the Cheney clan. "The Cheneys have always done everything as a family," says Bill Thomson, a Cheyenne lawyer and...