When most people think of politicians campaigning for the highest office in the land on late-night talk shows, the first image that comes to mind is probably Bill Clinton’s legendary visit to Arsenio Hall. He played the sax with the house band, while wearing a pair of Blues Brothers sunglasses and although it’s never been proven that his visit paved the way to the White House, it sure didn’t hurt.

It has just been announced that Jeb Bush will appear on The Tonight Show with Jimmy Fallon on 16 June, a day after the dynastic political heir and former Florida governor is likely to announce his candidacy for the Republican nomination in the presidential election. Based on the history of such appearances, it could go very well – or very, very poorly.

While Clinton is what springs to most people’s minds, the first two candidates to appear on late-night talk shows were John F Kennedy and Richard Nixon, who both appeared on Jack Paar’s Tonight Show in 1960. Clinton wasn’t even the first to play an instrument. Nixon appeared on the show again in 1963 and played the piano with the band. No sunglasses though.

Such appearances can humanise a candidate or reach a segment of the population that isn’t reading the daily newspaper or watching Meet the Press. Racked with the public thinking he was too wooden, Al Gore made fun of himself and his claim that he invented the internet by reading the Top 10 list on David Letterman in 2000. Mitt Romney tried the same tactic in 2011 and joked about his hair on the show. While these were successful appearances, they weren’t eventually successful for either man’s run at the office. However, George W Bush also read the Top 10 list in 2000 and delivered a groaner of a joke about Letterman’s recent heart surgery, and we all know how that turned out. (Thanks again, Florida.)

But criticism of such stunts can often outweigh the positives. In 2009 Barack Obama was the first sitting president to appear on late-night when he visited Jay Leno on The Tonight Show. He made an off-color joke about the Special Olympics and later had to apologize. Every candidate who goes on late-night faces the criticism that the appearance is just mere fluff. Even as recently as 2012 when Obama slow-jammed the news with Jimmy Fallon, Fox News had a field day with his appearance, insinuating that it was beneath the office to appear on such a program.

This was especially true when John McCain announced his candidacy for president on The Late Show in 2007, the first presidential candidate to do so. Arnold Schwarzenegger, a regular on The Tonight Show, announced he would run for governor of California on the show in 2003, but back then it seemed like an actor in a joke candidacy rather than a serious politician trying to go Hollywood.

While Letterman welcomed McCain in 2007, he mocked the politician relentlessly the next year when McCain cancelled an appearance on the show at the last minute. When he appeared later that year to make up for the snub, Letterman got out the hardball questions, which made for quite an uncomfortable visit (though one for the record books). Letterman was also tough on David Cameron, the first sitting PM on American late-night TV, but it was unintentional. Cameron failed to answer Letterman’s questions about when the Magna Carta was signed and who composed “Rule Britannia”. He even joked on the air that Letterman had ended his career.

Prime minister David Cameron got more than he bargained for when he went on David Letterman. Photograph: Stefan Rousseau/PA

Michele Bachmann was also unintentionally humiliated in 2011 when she showed up on Late Night with Jimmy Fallon and the house band The Roots played her on with the song “Lyin’ Ass Bitch”, which almost got bandleader Questlove fired from the show. Usually Bachmann does a very fine job of embarrassing herself without help from some ornery musicians.

But nothing was more embarrassing as what John Kerry did to himself on The Tonight Show in 2003, riding up to Leno’s desk on a (borrowed) Harley wearing a leather jacket and jeans. He looked like what every candidate who appears on a talk show fears: a man trying too hard and looking like he’s pandering.

Of course Kerry talked mostly politics with Leno, just as Clinton talked about racism with Arsenio Hall, and every politician talks about their agenda and why they would be the best choice for office. But that’s never what we remember or judge. It’s always what they wore, the instrument they played, or the poor joke they made. It’s never about substance, it’s all about image. Jeb Bush should keep that in mind before he goes on The Tonight Show. He should work harder at figuring out how to not embarrass himself than worrying about policy initiatives.