In a recent episode of Jerry Seinfeld's web series Comedians in Cars Getting Coffee, the famed comic met with the president of the United States — the man entrusted with the nuclear weapons codes and the like — and asked him about his underwear.

"How far can you wander around up there in your underwear, how far can you get before there's like people and it's not cool," asked Seinfeld on a walking tour of the White House with Barack Obama.

"It's not cool generally wandering around in my underwear," the president said, playing the straightman.

"If I slid open your underwear drawer — one brand or a number of brands?"

"You gotta go with one brand," said Obama deadpan.

That the president would be asked questions about his undergarments shouldn't surprise Seinfeld fans, considering his comic penchant for focussing on the minutiae of daily life.

But going along with the gag in a presidential setting can raise questions about how far leaders can go before they risk sullying the dignity associated with high office.

"Every White House has this debate between the media advisers who are pushing for this because they count the number of hits, the amount of exposure that it gets, versus the more policy-oriented people who are concerned because this is a person who is making life and death decisions, making peace and war decisions," says Gil Troy, a McGill University history professor and author of the new book The Age of Clinton: America in the 1990s.

Justin Trudeau and Sophie Grégoire-Trudeau in Vogue

Canadian Prime Minister Justin Trudeau and his wife, Sophie Grégoire-Trudeau, were featured in the January issue of Vogue. (Norman Jean Roy/Vogue)

As he sees it, "there should be a kind of gravitas, there should be a certain kind of decorum, there should be a certain kind of distance surrounding the office. And it's very hard to do that in an age of popular politics, in an age of popular culture."

Vogue photo shoot

It's an issue that has already confronted Canada's newest prime minister, who just a couple months after taking office caused a stir for his unconventional, almost sultry photo shoot in the fashion magazine Vogue.

That he agreed to such a shoot was one thing, but being shown in an intimate embrace with his wife, Sophie Grégoire-Trudeau, his hands firmly clasping her behind, was an image Canadians were not used to seeing from their leader.

Trudeau made no apologies for the photos, arguing that hard news publications are not the only venue for Canadians to get to know their leader.

"People get their news through a variety of sources. And for a lot of people, certainly in the United States, reading that Vogue article will have been the only thing they see about Canada or Canadian politics all year," he told The Canadian Press.

This desire, to be more accessible to different forms of pop culture media, has certainly been embraced by Obama. 

Sitting presidents had previously dipped into the unconventional — Richard Nixon appeared on the variety show Laugh-In, for example, while Gerald Ford pre-recorded an introduction to Saturday Night Live. And presidential candidates have appeared on late night talk shows in the runup to the election.

Yet Obama became the first sitting president to appear on a late-night talk show, when he became a guest on the Tonight Show with Jay Leno in 2009.

And it was just one of a slew of appearances he has made with pop and comic hosts such as Jimmy Fallon, (in which he "slow jammed' the news), Stephen Colbert, Jimmy Kimmel, Conan O'Brien, Oprah Winfrey, Ellen DeGeneres and Steve Harvey, as well as on shows like The View, Live With Kelly and Michael, Access Hollywood, Entertainment Tonight, Myth Busters, Funny or Die's Between Two Ferns with Zach Galifinakis, and, most recently, the reality show Running Wild with Bear Grylls.

Obama Power of Persuasion

Obama with actor-comedian Zach Galifianakis during an appearance on 'Between Two Ferns.' (Funny or Die/Associated Press)

These appearances have become fodder for some conservatives, who believed they were unbecoming of the leader of the free world. But even comedian David Spade, not exactly known to wade into political issues, commented on Obama's recent appearance on the reality show Bear Grylls. 

'It's just too much'

"A president should have a little more dignity," Spade told TMZ.  "I realize Woodrow Wilson went on Dancing with the Stars once," he joked.

"But what president is doing reality shows? It just sounds weird to me. It's just too much."

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Prime Minister Stephen Harper invited comedian Rick Mercer to 24 Sussex Dr for a skit on CBC's Rick Mercer Report. (Deb Ransom/PMO)

When Obama appeared on Zach Galifinakis's web show, ostensibly to promote his new Obamacare health-insurance, Mike McCurry, the former press secretary to Bill Clinton, cautioned that one does have to "worry about the dignity of the presidency."

"There's a limit to how much you can do," he told the New York Times.

Canadian prime ministers, of course, haven't had the same access to late night talk fests, although Jean Chrétien did appear on the now defunct Open Mike with Mike Bullard Show and participated in certain CBC's comedy shows. Prime ministers have also generally played along when ambushed by cast members of This Hour Has 22 Minutes.

Chretien also ate hamburgers with CBC's Rick Mercer, while Paul Martin went Canadian Tire shopping with the comedian and Stephen Harper invited him for a sleep over at 24 Sussex.

"I do very much respect the need to trigger a democratic conversation," Troy said. "The fact that there's so much noise out there makes it really hard for the president or prime minister to get noticed."

But at the same time, national leaders must also think about the most difficult decisions they have to sell to the public, and how much they have made themselves less of an authority figure because they've become so familiar, he said.

"There's a kind of delicate balance there. And it does feel recently it's been lost."