Christie made his first appearance on Letterman's "Late Show" in New York Monday.
As he walked out onstage, Paul Shaffer and the CBS Orchestra played "Thunder Road," a song by New Jersey icon Bruce Springsteen.
"How do you feel about me?" Letterman asked Christie.
"I love you, Dave," Christie laughed. "No, no, a love that I have a difficult time really explaining, but a deep and abiding love."
"Well, now, now, we have a real problem," Letterman said. "But I've made jokes about you, not just one or two, not just ongoing, here and there, intermittent..."
Pulling a doughnut from his suit pocket and eating it, Christie quipped, "I didn't know this was going to be this long."
"All kidding aside, is it an issue or is it not an issue? And you tell me how you see things," Letterman said.
"Well, I only care if you're funny. I mean, from my perspective, if the joke is funny, I laugh, even if it's about me. If it's not funny, I don't laugh. But I've never felt like it was, you know, anything that really bugged me all that much, no," Christie assured Letterman, then telling the "Late Show" host he finds about 40 percent of his jokes about him funny.