"I got in the car this morning and the navigation lady wasn't speaking to me," he cracked. Keeping up the patter, Letterman added, "There's a possibility that I will be the first talk show host impeached," an reference to former president Bill Clinton's fling with a White House intern.
Guest Steve Martin also took a jab at the comedian.
"I was going to come out and make a few jokes, but it's really not funny -- a little bit, a little bit funny," he said, "but I do think that the one thing that will come out of this mess that has come out already, it proves that you are a human being and, you know, we weren't really that sure before."
Letterman told his audience that he "has his work cut out for him" in dealing with the fallout from his on-air confession.
Shargel, Halderman's lawyer, told "Good Morning America" Monday that Letterman's on-air confession last week was hardly the final word on the matter.
"Joe Halderman was at CBS for 27 years. Here's a guy who was an investigative journalist for so many years," Shargel said. "To say he was trapped in an extortion plot was kind of preposterous."
"I'm here to say, not so fast," Shargel said. "I look forward to cross-examining David Letterman, because I don't think the full story is before the public. There's much more to this story."
Freed on $200,000 bail, Halderman faces up to 15 years in state prison if convicted.
Last week, Letterman revealed to the studio audience that he'd received a package three weeks ago containing a threat to reveal those indiscretions if he didn't pay up.
In a press conference last week before Halderman's arraignment, Manhattan District Attorney Robert Morgenthau said Halderman demanded to be paid $2 million in an initial meeting with Letterman Sept. 9, when Halderman allegedly waited outside Letterman's New York City apartment.
Halderman had threatened to reveal "personal and private information" if Letterman did not accede to his demand to purchase a one-page screenplay he presented at the initial meeting, said Morgenthau.
The district attorney said the screenplay described a scenario in which Letterman's world would "collapse all around him" and would lead to a "ruined reputation."
Three subsequent meetings between Letterman and Halderman were recorded by Letterman's attorney, Morgenthau said.
Shargel told "Good Morning America" that he had not yet had a chance to hear the tapes that prosecutors say prove his client tried to extort Letterman, nor read the transcripts.
And while Shargel admitted that Halderman did attempt to cash Letterman's phony $2 million check, "the surrounding circumstances are what's relevant," Shargel said.
ABC News' Eileen Murphy, Michael James, Brandon Bodow and Richard Esposito contributed to this report.