"I screwed up."

That was John McCain’s admission to David Letterman last night after weeks of the late-night talk show host railing against the Republican presidential hopeful for canceling on him to deal with the economic bailout – but then doing an interview with Katie Couric of CBS.

The feud between the two men essentially ended last night.

Letterman immediately asked McCain: "Can you stay?"

"Yes, sir," McCain said. "Depends on how bad it gets."

"I have a son in the Marine Corps and I asked him to FedEx his helmet and flak jacket but it didn’t get here" in time, he added.

"I’m willing to put this behind us," Letterman said after poking a bit more fun at the White House hopeful.

McCain also promised to come back to the show if he’s elected president – Secret Service and all.

McCain also apologized to Joe Wurzelbacher – a.k.a. "Joe the Plumber" - the undecided voter the Arizona senator mentioned in Wednesday night’s debate who’s become an overnight media sensation.

"Joe, if you’re watching, I’m sorry," said McCain, who called average Americans, like Joe, the "victims of a drive-by shooting by Washington and Wall Street." McCain said he hasn’t spoken personally to Wurzelbacher.

McCain also talked about his running mate, Sarah Palin, saying the Alaska governor was "absolutely" his first choice, even though he didn’t knew her personally – just knew her reputation.

"In all due respect, one of the people I admired most was an obscure governor of a southern state called Arkansas and he turned out to be a fairly successful president," McCain said. "I mean, Ronald Reagan was a cowboy, no experience in international affairs. So, look, I think she has shown leadership."

McCain said he expected that Palin would appear on "Saturday Night Live" before the election ended. In fact, she "probably get more of an audience than our debate did." He said the chances of Palin coming on Letterman’s show are "very good," even though there are only 18 days left in the campaign.

The "Late Show" host then asked McCain about his accusations regarding Barack Obama’s relationship will Bill Ayers – a Vietnam-era domestic terrorist. He then asked McCain: "Did you not have a relationship with Gordon Liddy? Did you not have a fundraiser at his house?"

Liddy was the chief operative for President Nixon’s White House "plumbers" unit that broke into the Democratic National Committee’s headquarters at Watergate in 1972. That scandal eventually led to Nixon’s resignation in 1974. Liddy served four-and-a-half years in prison for his role.

"I know Gordon Liddy, he paid his debt … I’m not in any way embarrassed" to know Liddy, McCain said.

Letterman: "You understand the same case could be made with your relationship with him [Liddy] as [Obama’s] with Ayers."

Click here to watch a portion of the McCain interview on the "Late Show."