Must read: Could Palin flap be Letterman's Hugh Grant moment?

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 this 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 of 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?'