Letterman tours the John F. Kennedy Library in 2013 with his wife, Regina Lasko, and son, Harry. (Michael Dwyer/AP)

For years, he fought with his girlfriend, Regina Lasko, 56, about starting a family. She even dumped him at one point. His resistance, he admits, was that he felt he couldn’t do the show and be a father.

Then, in 2003, they had Harry, named after Letterman’s father.

“And then the minute the kid is born I realize: Holy s—, I have made an enormous mistake and tried to defend it for 15 years now,” he says. “I was wrong. I could not have been more wrong.”

Letterman and Lasko, who were married in 2009, spend summers in Montana, where there’s good fishing and enough space to teach the kid how to drive a stick. During the school year, they’re in New York for Harry. As the years pass, Letterman remains grateful that he’s been around to watch his boy growing up.

Letterman likes to tell Harry stories, even if they don’t always wrap up in a bow.

Take a recent Saturday morning when he and Harry went to see “Battle of the Sexes,” the dramatized account of the Bobby Riggs and Billie Jean King celebrity tennis match.

“It’s a very good movie, but what hadn’t occurred to me is that it’s a lesbian love story,” Letterman says. “So you see a lot of good-looking girls in their underpants making out.”

He stares straight ahead.

“We’re both eating our popcorn. ‘Uh huh. I see. Okay.’ Then it would go away and we could breathe again.”

He thinks back 60 years to a fishing trip he took with his own father. Somewhere along the way, they stopped to use a bathroom. Young Dave spotted a prophylactic machine on the wall.

“And I came out and said, ‘Jeez, there’s a machine in there. It’s not candy. It’s not cigarettes.’ And my dad said, ‘Ah, one day you and I are going to have that talk.’ And we never did.”

This brings a big cackle and he relates to his own son.

“I always think of that and I pester Harry. ‘Have we had the talk? We should. Especially now. Let’s have the talk.’ ”

His voice trails off and he laughs again. David Letterman knows there’s still time.