Updated at 1:37 p.m. ET on 7/17
Washington (CNN) – A GOP challenge from Liz Cheney could backfire, her new rival Sen. Mike Enzi suggested Wednesday.
The third-term Wyoming Republican said his constituents would stick with him through a primary - despite Cheney's wide name recognition and promise of a newer, younger conservative message.
"I'm absolutely not too old to be senator. I'm the median age," he argued in an exclusive CNN interview Wednesday.
"People in Wyoming don't believe in long campaigns," he continued. "In fact they complain about long campaigns. It doesn't take them long to make up their mind. And it doesn't cost a lot of money to have them make up their minds."
While he's been doing constituent events in the state for years, Cheney's never been to one, he said.
"She's never been to any of my listening sessions. I've done listening sessions in Wyoming where I actually listen to what the constituents have to say. I'm an old shoe salesman. I listen to the customer, I know who the customer is. I see how what fits with the inventory we've got, which is the legislation. I love to legislate."
Cheney, the daughter of former Wyoming congressman and Vice President Dick Cheney, announced on Tuesday she was launching a bid for U.S. Senate. In a video, she didn't mention Enzi by name, but proclaimed it was time for a "new generation of leaders to step up."
Enzi, 69, disputed the notion he's extended his stay in the Senate, correctly pointing out that he's pretty close to the upper chamber's median age (which stood at 62 before 67-year-old Ed Markey was sworn in as Massachusetts' newest senator on Tuesday). Cheney is 46.
" I'm in really good health, I'm on the committees that I want to be on. I have seniority, which is really trust that you develop," he said. "If somebody new comes in, you don't trust them. I've developed trust on both sides of the aisle, people trust me that what I say I'm going to do, I do."
The proof that voters will stick with him, he said, was in the talks he's had with voters during his decade-and-a-half in office.
"I don't have to do a poll. I've never done a poll. I can tell from the conversations I've had," he said.
As for Cheney, Enzi withheld any major blows, saying only that his new rival surprised him with the timing of her announcement.
"I'm only surprised in that she said if I ran, she wouldn't. She announced 30 minutes after I more specifically stated my intention," he said.
A source close to Cheney, however, told CNN she informed the senator she was considering a run before her announcement. The source added that Cheney had been to every county in Wyoming and would focus her run on Obama's record, rather than going after Enzi specifically.