NEW YORK — Sarah Palin would no doubt be horrified by the idea, but there's a chance she could become the same boon to David Letterman's career that Hugh Grant was to Jay Leno's.

Grant's 1995 appearance on NBC's "Tonight" show after a prostitution arrest, where Leno famously asked "what were you thinking?," was seen in retrospect as a turning point in the late-night race. It drew a huge audience and propelled Leno to the top of the ratings, a spot he would not relinquish.

Letterman did not court last week's battle with Palin, who called him "perverted" for making a joke about her daughter getting "knocked up" by New York Yankee Alex Rodriguez, and he said in retrospect the remark was in poor taste.

Palin rebuffed his invitations to appear on the show, but that might not matter. The story had the effect of turning the attention to Letterman at a critical time, during the second week of his new competition with Leno's replacement, Conan O'Brien.

"It will be interesting to see if that can be maintained or whether it is one of those temporary things," said Robert Thompson, director of the Center for the Study of Popular Television at Syracuse University.

The final numbers won't be out until later in the week, but there's a strong chance that Letterman could average more viewers than the "Tonight" show in the second week of O'Brien's new 11:35 p.m. job. That hasn't happened since 2005, and the timing is significant: some of Leno's old fans may be more amenable to searching for a new late-night habit during the transition period.

It's difficult to tell whether Letterman received a boost last week because of people interested in what he was going to say about Palin. Strong guests like Julia Roberts and Denzel Washington were a boost, too.

Letterman has referenced the NBC transition in a handful of jokes over the past two weeks, many of them poking fun at himself as much as his rival.

"Conan O'Brien, of course, is the new host of the 'Tonight' show,' " Letterman said a week ago. "Did they even look at my audition tape?"

On a top 10 list of Signs It's Time for Kim Jong Il to retire was No. 2: "Republic already named his successor, Conan Jong Il." Topping the list of Surprising Facts About Sonia Sotomayor was: "Demonstrated impeccable judgment by watching Conan."

Despite the competition, no doubt it's hard for Letterman to exhibit the same animosity toward O'Brien as he did toward Leno. O'Brien has openly acknowledged his debt to Letterman, and his subversive anti-talk show style is more reminiscent of what Letterman did in the 1980s than what Letterman is doing today.

Letterman maintains his biting sarcasm, but at age 62 he has evolved into more of a traditional talk show host than his rivals. Thompson said he believes Letterman is more topical than ever, in part a recognition of Jon Stewart's success at Comedy Central. The Letterman of two decades ago attracted attention for dropping watermelons from the roof of a building or wearing a Velcro suit; now he gets it for charged interviews with John McCain or Joaquin Phoenix.

When Letterman did a brief filmed skit last week tied to Washington's new movie, "The Taking of Pelham 1 2 3," it seemed like a quaint throwback; O'Brien does such pre-filmed segments all the time.

"David Letterman's biggest problem is he was brilliant in going against the grain," Thompson said. "David Letterman is now the grain. He's his own toughest act to follow. So that's why it is smart that he has tried to change the game."

Letterman, who went through a life-changing heart surgery and became a father in the past decade, seems committed to the new competition. It was revealed last week that he had agreed to a contract extension that will keep him on the "Late Show" into 2012, and there's no indication that he's looking toward retirement.

His longevity, however, may be his biggest handicap in getting back to the top. "By and large, late-night comedy is a young wise-guy's business," Thompson said.

The fans who thought he was fabulously hip in the 1980s now have their own teenagers looking to make their own late-night TV habits.

But it would be foolish to count him out. Palin may have inadvertently given Letterman a platform at a time when it is most valuable; the next few weeks will show how he's been able to use it.