And today the Cheney family includes Mary's partner of 14 years, Heather Poe.
"She is smart, she is funny, she is probably the most generous person I've ever met," Cheney said of Heather. "Since my dad was first nominated, she has been my rock."
But what is it to be Mary Cheney inside her parents' Republican party -- a party that opposes civil rights legislation protecting gays? A party that says in its platform that homosexuality is incompatible with military service?
If her father weren't vice president, would she still be a Republican? Cheney says she doesn't like to answer "hypothetical questions."
But she does say that if her father weren't on the ticket with Bush in 2004, she would still support the president.
"I think he's a very good man," Cheney said of Bush. "On these issues, he hasn't caught up."
Cheney is now back in private life, working at AOL and says inside her family, she and Heather are free to be themselves in love. Sawyer asked Cheney if she and Heather planned to marry.
"Well, from my perspective? Heather and I already are married," she said. "We have built a home and a life together. Um, I hope I get to spend the rest of my life with her. The way I look at it, is we're just waiting for state and federal law to catch up with us."