A witless and undignified stunt? Or an amusing and effective public-relations exercise?

Opinions differed on Barack Obama’s parody interview with comedian Zach Galifianakis on the website Funny or Die last week, and not just along party lines. Dan Pfeiffer, a top Obama strategist, told The New York Times that even within the West Wing there were debates about how unconventional the president could be in trying to promote his message to young people. Staffers joked that some of the more outrageous gambits “were going to give David Gergen a heart attack.” Gergen, a longtime Washington insider who has advised presidents of both parties, most recently Bill Clinton, hasn’t gone into cardiac arrest, but he did confirm that he’s “no fan of presidents appearing on shows” like Galifianakis’s. Mike McCurry, who spent four years as Clinton’s press spokesman, likewise cautioned that Obama should “worry about the dignity of the presidency.”

You know things are bad when even former Clinton loyalists think Obama is demeaning the nation’s highest office.

The president went on Funny or Die to plug the Affordable Care Act and urge young adults to enroll at HealthCare.gov. Administration officials wasted no time declaring the show a success. Within hours after being posted, more than 9 million people had viewed it, and ObamaCare spokeswoman Tara McGuinness tweeted that it had become “the #1 source of referrals to HealthCare.gov,” more than 32,000 before the end of the day.

Mission accomplished? Maybe so, but at the price of being mocked in a faux interview by a crude entertainer whose shtick involves insulting his guest with boorish questions. Where will Obama build his presidential library, Galifianakis asked, “in Hawaii or your home country of Kenya?” If Obama had a son, would he be interested in football or be “a nerd like you?” Affecting utter boredom as the president made a plug for ObamaCare, Galifianakis sighed: “Is this what they mean by drones?”

There was a time when presidents understood that their position demanded a certain gravity. That the nation’s chief executive was not just another celebrity, but the custodian of unique constitutional authority. That when you live in the White House and fly on Air Force One and everyone stands when you enter the room, it isn’t appropriate for you to pander to the lowest common cultural denominator.

Exactly where the line should be drawn has always been something of an open question. “I think the American public wants a solemn ass as a president, and I think I’ll go along with them,” Calvin Coolidge once said, explaining his taciturn style. Yet he didn’t balk at donning a feathered Sioux headdress during a trip to South Dakota in 1927, overruling advisers who feared he would appear laughable. Remarked Coolidge: “Well, it’s good for people to laugh, isn’t it?”

In truth, most Americans don’t want their presidents to be solemn asses. But they are expected to “maintain the dignity of office,” as George Washington told James Madison, while simultaneously avoiding the “imputation of superciliousness or unnecessary reserve.”

It’s a balancing act, and as public mores evolve, so do notions of presidential propriety. For a long time presidents were especially careful to respect the “dignity of office.” Their more recent successors take greater pains not to be accused of “unnecessary reserve.” Harry Truman wore a coat and tie when he went out for his “daily constitutional.” Bill Clinton and both George Bushes saw nothing wrong with publicly jogging in shorts and sweaty T-shirts.

But even in our anything-goes era, there ought to be limits. When Clinton, on MTV in 1994, was asked whether he wears “boxers or briefs,” he should have responded with an icy stare, and called on another questioner. Instead, grinning, he revealed his preference in underwear.

That crossed a line that should have been inviolable, degrading not only Clinton but the respect owed to the presidency. Fourteen years later, when the same question was posed to candidate Obama, he knew better than to dignify it with a substantive response. “I don’t answer those humiliating questions,” he said.

He should have said exactly the same thing when he was asked to go on Galifianakis’s insult-slinging interview show. It may have been a hip, edgy way to drive traffic to the ObamaCare exchange. But it also diminished the president and the nation he represents. There are better ways to get hits on a website.

(Jeff Jacoby is a columnist for The Boston Globe).