President Obama’s visit to the Late Show with David Letterman was a fascinating media summit-meeting. Each had something to promote: Obama, his policies and the assurance that he’s on top of challenges such as the struggling economy and health-care reform; Letterman, his interviewing sharpness and the assurance that he’s on top of challenges such as being ratings-dominant and as pop-culturally influential as Conan O’Brien and Jon Stewart.

Obama recycled many of the talking-points he used during his blitz of the Sunday-morning political shows, emphasizing that the economy is improving, that the stimulus package was necessary and a success, that problems remain but “we’re going to come back stronger than before.”

The context, of course, was different. Instead of, say, ABC’s George Stephanopoulos, who tooted his own horn about asking “tough questions” of the President, Letterman presented himself as that tricky combination of Midwestern voice-of-the-common-man and show-biz power-wielder that serves him so well. Letterman’s brisk questions enabled Obama to clarify some of what he called “a lot of the misinformation out there… that’s why I’m on the Dave Letterman show.”

The host followed that up with: “The one idea I’d like to see right away are those death panels. If we could get those in place right away…” he said, both men cracking up at the absurdity of the foolishness that surrounds what the President is trying to accomplish.

Lest any viewer doubt where Dave stands these days, his opening monologue was peppered with potshots. “President Bush,” he noted, never appeared on the Late Show, because “he was always too busy not-working.” Relax, he also told the studio audience, “the building has been cleared of all Republican congressmen.” The folks in the seats let us know where they stood, too: They greeted that comment with huge applause.

You’ve probably already read the salient sound-bites. Addressing the notion that some of the current displeasure with the President is racially-motivated, Obama said drolly, “I was actually black before the election.” He also noted, “One thing you sign up for in politics is that folks yell at you.”

All in all, both men ended the hour seeming strong and in control. “I can’t tell you how satisfying it is to watch you work,” Letterman said in closing. To which I could add, “Back at you, Dave.”

Did you watch Letterman and the President? What did you think?