Gov. Beshear weighing 2028 Democratic bid for presidency

"Your name frequently comes up as a contender for the 2028 Democratic primary for president. You said you'll think about it after next year," CNN host Dana Bash told Beshar. "What will make you decide that that's going to be a yes, you'll run for president?"

Beshear said he hoped the list of potential Democratic leaders would grow.

"If you asked me this question a couple of years ago, I would have said no. My family's been through a lot, but I do not want to leave a broken country to my kids or anyone else's. So, what I think is most important for 2028 is a candidate that can heal this country, that can bring people back together. So, when I sit down, I'm going to think about whether I'm that candidate or whether someone else is that candidate," Beshear added. 

The Democratic governor said he was going to make sure to put the country first. 

"I'm going to make sure we're putting the country first, because my kids deserve to grow up in a country where they don't have to turn on the news every morning, even when they're on vacation and say, what the heck happened last night?" he said.