"We need to re-energize the base, rejuvenate our party and attract new talent, bring along the next generation. That's kind of the reason she's running," he said.
"Some of our best leaders are revolutionaries," he added.
But in an appearance Monday on NBC's "Today" show, the former vice president wouldn't commit to stumping for his daughter on the campaign trail.
"Well, I'll do all I can," Cheney said. "Probably the best thing I can do is stay out of the way. I'm part of that generation. My time is up, I had a great time, but we really do need new talent. Here we have a woman with five children, who has got the drive and the energy to represent that next generation and we need to be passing on leadership in the party to that next generation."
Liz Cheney out-fundraised Enzi in the most recent quarter, although the incumbent senator often polls ahead of his opponent and is seen as the frontrunner in the race.