Timing is everything in comedy -- but was President Obama missing his cue with a late-night TV appearance in the middle of an economic crisis?

Obama, who is in California for a set of town hall meetings, appears Thursday on "The Tonight Show With Jay Leno." 

Though late-night shows are a staple nowadays for any political candidate, traditionally they've been avoided by anyone in the Oval Office. The Leno visit marks the first such appearance of any sitting president. 

And with the markets still well below their highs and the sudden firestorm over bonus pay at AIG, critics suggest Obama might be showing a little tone-deafness by heading to Hollywood. 

"It's not an accident that no sitting president has ever done a show like this," media analyst Steve Adubato told FOX News.

Obama didn't shy away from typical late-night banter with Leno, joking about his bowling skills and the clothes worn by Leno's band leader, Kevin Eubanks, but the president also discussed a range of hot issues in Washington, from AIG bonuses to the performance of his treasury secretary.

Adubato noted the difficulty any commander-in-chief would have balancing levity and seriousness in that Los Angeles setting at a time of crisis.

"I'm not convinced this was the smartest move," he said Thursday before Obama's TV appearance.

Leno's not the only sticking point. After the president released his NCAA tournament picks, Duke coach Mike Krzyzewski wondered aloud why Obama was spending time on brackets when more pressing matters are at hand. 

"As much as I respect what he's doing, really, the economy is something that he should focus on, probably more than the brackets," Krzyzewski said. (Obama picked Duke rival North Carolina to win the NCAA Championship.)

Democratic strategist Dan Gerstein said Obama, as he did during the campaign, is just trying to connect with as many Americans as possible -- and using every platform available, be it "The View," the Sunday morning talk shows or Leno. He saw no tonal problems with a guest appearance on late night. 

"I think he's trying to project an air of normalcy and reassure people that they're working hard, at the same time that this is not a time for panic," Gerstein said. "As long as he doesn't do something that's jarringly discordant on 'The Tonight Show,' it's going to be fine." 

Dan Amundson, research director at the Center for Media and Public Affairs, said Obama might just be squeezing in an appearance before Leno leaves the show later this year -- but he said the show could play in his favor as he tries to sell his economic agenda. 

Obama embarked on a similar public campaign, on the stump and in the media, last month when he was trying to build support for his economic stimulus plan. 

"Part of me says it's great a president is using every avenue to talk to everybody he can," Amundson said. "On the other hand there is always the potential of losing political gravitas and stature." 

He said that dilemma dates back, at least, to Bill Clinton playing the sax on "The Arsenio Hall Show" during the 1992 presidential campaign. 

Though the Arsenio appearance was seen as a plus for Clinton, former President George W. Bush got caught in a jocular jam in 2004 when, at a media dinner, he cracked jokes about not being able to find weapons of mass destruction in Iraq. Too far, critics said. 

Mary Kate Cary, a speechwriter for former President George H.W. Bush, wrote in a U.S. News & World Report column that Obama's Leno appearance could be damaging. 

"There's a reason presidents don't do comedy on television, especially in tough times," she wrote. "Doing Jay Leno lessens the stature of the office, and diminishes the man. On Leno, he becomes just one more talk show guest." 

With outcry building over revelations that bailed-out AIG was distributing $165 million in bonuses, Obama has tried to assure the public he still appreciates the somber mood of the country.

"I know a lot of you are outraged about this. Rightfully so. I'm outraged, too," he told the crowd Wednesday at a town hall meeting in Costa Mesa, Calif.. "Listen, I'll take responsibility. I'm the president." 

No one at the town hall meeting asked Obama a question about AIG, and the White House said the questions are not pre-screened. But the AIG flap apparently is on the minds of most Americans: A Rasmussen Reports poll shows most Americans are following the controversy, and 76 percent of Americans want the employees who received bonuses to give them back. 

FOXNews.com's Judson Berger and The Associated Press contributed to this report.