Just how powerful is a comic’s punch?

On its face, it wouldn’t seem to be a good thing. You’re the president of the United States, running for a second term, and some of the most popular commentators on television are depicting you as a dimwit and a vacation-loving slacker who lets your No. 2 guide the ship of state.

It wouldn’t be the profile that White House image-maker Karl Rove would choose for George W. Bush, but it’s the one the president seems to be stuck with, courtesy of Jay Leno, David Letterman, Jon Stewart and other TV comedians.

Bush, in fact, was the target of more than three times as many jokes on late-night television during the first four months of this year as the expected Democratic nominee, Sen. John F. Kerry of Massachusetts, according to a media watchdog.

The comedians and their handlers say that’s typical of the attention drawn by an incumbent. They also acknowledge that, while they have settled on a caricature of Bush, they are only beginning to fix on Kerry, as waffling, dull and out of touch.

But political analysts, presidential historians and media watchers say that the stereotypes of a less-than-brilliant, distracted chief executive often work to Bush’s benefit.

Stuart Stevens, a Republican consultant for Bush and an accomplished writer of essays, fiction and television programs, said the majority of Americans don’t take to heart the opinions of late-night comedians or others they see as part of the East and West Coast elites.

“People who are interested in voting for this president don’t need the Good Housekeeping seal of approval from people who hang out in Cambridge,” Stevens said.

“I think one of the standard problems that Republicans had with [former President] Clinton was that they condescended to him and didn’t understand his appeal,” Stevens noted. “And I think that is one of the big failings the liberal intelligentsia has with Bush, they condescend to him intellectually.”

Kathleen Hall Jamieson, director of the Annenberg Public Policy Center at the University of Pennsylvania, thinks the TV comics in particular can hold tremendous sway but that the effect of their jokes is not always obvious. “It’s very tricky to figure out the hidden inferences, whether someone is helped or hurt,” she said. “Some people look at this stuff, which suggests Bush is an ordinary guy who makes quick, instinctive decisions, and say, ‘Great!’ ”

The late-night circuit

Lest there be any doubt about the power of the late-night programs, consider that five of the Democratic presidential candidates this year went on “Late Night With David Letterman” to read top 10 lists, often poking fun at their own candidacies. Kerry, languishing in the polls in November, rode a motorcycle onto Leno’s stage in a leather jacket and jeans -- an effort to show he was a regular guy.

The punch line here is that voters -- particularly young ones -- get their political educations from TV comedians. In fact, more than half of voters under 30 learn about the campaigns from late-night or comedy shows, according to a recent survey. More than one-quarter of young voters said they learned things from those programs that they hadn’t gleaned from any other source.

While comedians may be near the heart of presidential discourse, the White House hardly seems preoccupied with monologues and top 10 lists.

The president’s supporters have taken every negative stereotype and found its happier corollary. Rather than “simple,” the Republican faithful describe the president as “clear-headed.” Instead of “stubborn,” they view him as “determined.”

They remind detractors that Ronald Reagan suffered many of the same slings and arrows.

“A goodly number of people seem to have concluded there is no problem there, and some number have regarded the president’s plain-spokenness as a positive factor,” said Bruce Buchanan, a University of Texas government professor who has followed Bush’s career since he was governor of that state. “They would say, ‘He means what he says and he says what he means.’ ”

Other observers said the observations of a few wags on the coasts don’t really change opinions of moderate Americans.

“When Hollywood figures attack President Bush at awards shows and other venues, that backfires with people in the heartland,” said Gary Bauer, a onetime presidential candidate and founder of the conservative American Values think tank.

Author Neal Gabler, who writes about the effect of celebrity and pop culture on American life, disagrees, saying the dumb jokes get at a truth about Bush that most Americans don’t want to hear.

“There is a deep strain of anti-intellectualism and a deep skepticism toward anyone who is a thinker in this country,” said Gabler, now a senior fellow at the Lear Center for the Study of Entertainment and Society at USC. “I think the White House finds some advantage in it. ‘He is not a pointy-headed intellectual, everyone,’ they imply. ‘He is just like you.’ ... He is not like John Kerry, speaking French fluently.”

The ‘b’ word: ‘brainy’

From the founding of the republic until the present, candidates perceived as too brainy often have suffered.

Andrew Jackson defeated John Quincy Adams in 1828 and birthed the modern Democratic Party, with supporters chiding the incumbent: “Adams is a writer, Jackson is a fighter.” In the middle of the last century, the bookish Adlai Stevenson was belittled as a weakling, compared with war hero Dwight D. Eisenhower.

But Buchanan, the Texas historian, said it is overly simplistic to label the president or his followers as anti-intellectual. “People in those red states, who vote for Bush, want their kids to go to college as much as anyone else,” Buchanan said. “I think that feeling has morphed. It’s become a culture war thing. To some people, ‘Eastern Seabord,’ ‘latte-sipping’ and ‘French-speaking’ mean that a politician is not likely in the right place on the culture issues that matter to them -- like abortion, gay marriage and stem cell research.”

The low-intellect rap against Bush -- who attended Yale University and Harvard Business School -- will only hurt the president if it is linked to other critiques, several White House watchers agreed.

Buchanan said a more serious threat to the president lurks in the content of several recent books by former members of his administration. They tend to depict Bush in “ideological, some might even argue irresponsible” terms, shortcutting serious policy discussions, Buchanan said.

Jamieson believes that if the public comes to view Bush as “stubborn ... stubborn plus stupid equals unqualified.”

The comics have been slower to get a fix on Kerry.

According to the Washington-based Center for Media and Public Affairs, it was not until April that the Massachusetts senator finally passed former Vermont Gov. Howard Dean as the most popular late-night joke target among the Democrats.

Early returns from the comic precincts are beginning to flow in. They tend to register Kerry’s Ichabod Crane looks, his wealthy wife and, especially, his alleged tendency to flip-flop.

Leno said at a White House correspondents’ dinner last month that Kerry “could be the first president to give both the State of the Union address and the rebuttal.”

Letterman’s executive producer, Rob Burnett, said Kerry has presented “no great material yet. It will happen; it just hasn’t happened yet.”

In an interview, Leno -- like Letterman a political independent who takes pains to hide his leanings -- insisted that voters shouldn’t look to him for wisdom. “The real trick is not to know more than anyone else about the news,” said the host of the top-rated “Tonight Show.” “The key is to know exactly what everyone else knows.

“I don’t really believe you change anybody’s mind with comedy. You just reinforce what they already believed.... [Howard] Dean, fairly or unfairly, became the crazy, yelling guy. Kerry may or may not be the flip-flopping guy. We’ll see.”

In a mid-April monologue, Leno offered a quip about those who will choose the president. He asked his audience how many had watched Bush’s speech on Iraq and received a smattering of applause; then he asked how many had watched the final episode of “The Apprentice” and heard the crowd roar.

“See, that’s the problem right there,” Leno said, nodding impishly. “You get the government you deserve.”

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Comics take a bite in the sound bites

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The election has provided endless fodder for TV’s top wits. Here is a sample:

* “President George Bush’s approval rating has dropped to 46%. Let me put this in perspective: Saddam Hussein’s approval is rating is 49%. Forty-six percent! But Bush is not worried. That’s the kind of grades that got him through Yale, so he couldn’t be happier.”

-- David Letterman

* “President Bush launched a new wave of attack ads against John Kerry, where he accuses Kerry of being ‘wrong on taxes and wrong on defense.’ John Kerry responded with an ad that says: ‘George W. Bush: Wrong on all his SATs.’ ”

-- Conan O’Brien

* “We make jokes about it, but the truth is, the presidential election really offers a choice of two well-informed opposing positions on every issue. They both happen to be John Kerry’s.”

-- Jay Leno

* “[Bill Clinton] has a brand-new book coming out in the next couple of months, and the Democrats are worried that the Clinton book might upstage the Kerry campaign, and I’m thinking, ‘Hell! A day-old meatloaf might upstage that campaign.’ ”

-- David Letterman