Is David Letterman in danger of being Imus’ed?

The odds, admittedly, are extremely long that CBS Chief Executive Leslie Moonves will do to his late-night star—and, by the way, profit machine—the same thing he did to Don Imus over off-color quips about young women.

In April 2007, Moonves famously fired Imus from CBS Radio after the shock jock called the Rutgers University women’s basketball team “nappy-headed hos,” a racial-sexual bifecta that provoked a storm of outrage that couldn’t be quelled, even by Imus’ groveling to Al Sharpton.

Protesters held up placards reading “DIRTY OLE MAN” and “SHAME ON CBS,” while half a dozen voices shouted, “Fire David Letterman!”

But it’s almost unfathomable that Moonves would take Letterman off the air over the Sarah Palin flap, sparked by comedian’s ill-considered jokes about the Alaska governor and one of her teenage daughters—either 18-year-old unwed mom Bristol, as Letterman contends, or 14-year-old Willow, and his detractors insist.

On his show Monday night, in his second attempt to explain himself since he got into trouble last week, Letterman rejected CBS advice to stay mum and abjectly apologized to the Palins—and the governor seemed to accept his apology, although she left herself the option of keeping the story going.

None of this was enough for a self-described “diverse coalition of concerned citizens,” with the Web site www.FireDavidLetterman.com, that staged a ragtag rally Tuesday afternoon in front of the Ed Sullivan Theater, home of Late Show with David Letterman for the past 16 years, to demand the talk-show host’s head.

Cordoned off behind steel barricades across the street from the theater—and monitored by three cops and a couple of beefy security guys, one of them blowing bubblegum bubbles—the protesters held up placards reading “DIRTY OLE MAN” and “SHAME ON CBS,” while half a dozen voices shouted, “Fire David Letterman!” In a separate cordoned-off area down the sidewalk, a smaller group of Letterman supporters held up a sign reading “Sarah Needs a Life. Bristol Needs a Spouse. I See Idiots from My House.”

Palin ally John Ziegler, a Los Angeles radio host whose documentary Media Malpractice argued that biased liberal journalists trashed John McCain’s running mate, tried grimly to get a news conference started as passers-by and tourists mingled with the press.

Ziegler scowled as a huge red-bearded man carrying a placard reading “I’m a Right-Wing Lunatic” whirled around and shrieked such sentiments as “I hate it when people tell jokes on television!” “Jesus is speaking to me!” and “Letterman is worse than Hitler!” (Turns out the guy was a plant from the Ron & Fez Show on Sirius XM Radio.)

MSNBC and Air America were also represented, and Rupert Murdoch’s minions sent not one but two satellite trucks—one to provide live feeds of the spectacle to Fox News Channel and Fox Business News, and the other to service the local Fox station.

For anyone who has been living under a rock, Letterman joked last Tuesday night that the unnamed Palin daughter, while attending a Yankees game with Rudy Giuliani and her mother, “was knocked up by Alex Rodriguez.” He added that the young lady had also been hanging out with disgraced former New York Gov. Eliot Spitzer, who resigned his post last March over his penchant for hookers. Meanwhile, Letterman said, Sarah Palin was busy updating “her slutty flight-attendant look.”

On Monday night, Letterman manfully apologized “to the two daughters involved, Bristol and Willow, and also to the governor and her family and everybody else who was outraged by the joke. I’m sorry about it and I’ll try to do better in the future.”

Palin’s response was at once tepid and loquacious: “Of course it’s accepted on behalf of young women, like my daughters, who hope men who ‘joke’ about public displays of sexual exploitation of girls will soon evolve.”

Never one to lose an opportunity to share her views on a variety of topics, the governor went on: “Letterman certainly has the right to ‘joke’ about whatever he wants to, and thankfully we have the right to express our reaction. And this is all thanks to our U.S. military women and men putting their lives on the line for us to secure America’s right to free speech—in this case, may that right be used to promote equality and respect.”

From a tasteless joke about teenagers to a patriotic paean to servicewomen in harm’s way—this does not sound like a politician intent on putting an end to the story. Rather, Palin is leaving herself wiggle room to talk about it some more.

Likewise, the muted Moonves seems to be craving some wiggle room of his own. While Ziegler claimed on Tuesday that CBS “is showing support for Letterman by its silence”—and indeed booked and bumped him from CBS’ Early Show—Moonves has hardly been an openly loyal boss, let alone a profile in corporate courage, in the week since Letterman has been twisting in the wind.

“No comment,” a CBS spokesman told me Tuesday afternoon when I called to get Moonves’ take on the imbroglio. Likewise, the normally voluble Sumner Redstone, the 87-year-old executive chairman of CBS and Viacom, didn’t respond to my request for his views.

“They’re in a wait-and-see pattern,” Ziegler told me. “They’re waiting to see if they’re going to lose any money out of this.”

Already one sponsor, the hotel chain Embassy Suites, has dropped out of the Late Show, and an rally organizer was passing out fliers targeting additional advertisers.

In the meantime, Dave, it looks like you’re on your own.

Lloyd Grove is editor at large for The Daily Beast. He is also a frequent contributor to New York magazine and was a contributing editor for Condé Nast Portfolio. He wrote a gossip column for the New York Daily News from 2003 to 2006. Prior to that, he wrote the Reliable Source column for the Washington Post, where he spent 23 years covering politics, the media, and other subjects.