Well, it turns out that his affection for David Letterman goes pretty deep. And vice-versa, as his appearance on Friday was the last stand-up to appear on the show. But what was pronounced in the appearance is that about three-quarters of the way through, it's clear that, however acerbic his persona, he starts struggling with his performance, as he explains seeing Letterman as a 13-year old kid and repeats his favorite joke from that act that he's been telling friends for years. It's a wonderful final routine, and very touching.
In the comment section on YouTube, someone adds a bit to the story, having been in the audience. He writes,
"I had the tremendous fortune to be there live for this taping. After Norm exited and the credits finished rolling, Dave said to the crowd, 'If any of you here are aspiring stand-up comedians, and you can't do what you just saw on that stage...I don't know what to tell you because that is as fine of a stand-up performance as you're ever going to see.'
"Then Dave exited and announcer Alan Kalter walked on stage and said, 'I've just been informed that tonight was actually Dave's last show. There's no way we can follow that.' [BobNote: Obviously, Kalter was being facetious.] "When Norm started to choke-up for the second time, you could hear audible sobs in the theater. Really a huge emotional moment."
Here's the performance.