"There's a lot of sensitivity around Biden," notes Dana Carvey, the veteran comic who specializes in presidential humor. Mr. Carvey told me that for a while after the 2020 election, many liberal comedians felt they were in a "vise grip," squeezed between their own political views and the desire to get laughs. "Has politics gotten so serious and so entrenched that we have something bigger than our jokes right now?" he asks. "Some comedy writers feel they can't do something that will sabotage their party and let the bad guy get leverage. I don't think any of this is spoken out loud. It's just obvious."

A year ago, Mr. Carvey said, he asked some of Stephen Colbert's writers at CBS. "If Biden was a Republican, do you think we would go at him harder?" The response was, "That's a really interesting question." Translation: Yes.

America's media are as divided as its politics. Conservatives dominate talk radio and maintain a powerful presence in cable-TV news, while liberals are the kings of comedy. So it makes sense that there haven't been too many Biden jokes. Things have "loosened up a bit," notes Mr. Carvey, "but it's still a hot oven, and you're not sure you want to touch it."

The loosening began as Mr. Biden hinted at a second term—which some of his supporters in the comedy world don't think is wise—and continued when classified documents were found in his Wilmington, Del., garage. "Say it ain't so, Joe," cracked Mr. Colbert. "I know you're at retirement age. Are you starting a collection? They're classified documents, not spoons from the Delaware Train Museum!"

Though some presidents have been mocked more than others, they have all had to endure it. In the early 1900s, newspaperman Arthur Brisbane ridiculed the rotund William Howard Taft: "Justice Brewer of the Supreme Court said that ‘Taft is the politest man in Washington; the other day he gave up his seat in a streetcar to three ladies.'" As radio took hold, presidential humor increased, led by the acerbic Will Rogers, who observed, "Calvin Coolidge doesn't say much, and when he does, he doesn't say much." Television made Americans more aware of what their presidents looked and sounded like, leading to quips such as Bob Hope's about President Eisenhower: "The Democrats claim Ike plays too much golf, and the Republicans claim he doesn't play enough—and they have the scorecards to prove it."

The tempo increased dramatically in 1962 with Vaughn Meader's comedy album, "The First Family," which lovingly joked about John Kennedy and sold a remarkable 7.5 million copies. Harsher comedic portrayals were subsequently aimed at Lyndon Johnson, Richard Nixon and Gerald Ford. A few presidents, most notably George H.W. Bush and George W. Bush, embraced the jokes and befriended the performers, while three men, Ronald Reagan, Bill Clinton and Donald Trump, had so many mockable traits that the comedy market soared while they were in office.

The last Democratic president to be seriously roasted was Mr. Clinton, whose transgressions—ranging from overindulging at McDonald's to his affair with White House intern Monica Lewinsky—were too much for comedians to overlook. Moreover, there was little fear that jokes would wound Mr. Clinton, whose approval rating soared as high as 73%.

Joe Biden, on the other hand, has a job rating in the mid-40s, making some entertainers worry about his vulnerability. Darrell Hammond, who did a masterful job mocking Clinton on SNL, told me, "People today feel OK laughing at character-driven stuff—they feel like they don't have to choose sides as a Democrat or Republican."

Barack Obama's election created stress for some comics, uneasy about insulting the first Black president. Jay Pharoah, who played the role on SNL, felt he wasn't allowed to do enough with the character, recalling a directive from executive producer Lorne Michaels. "‘You got to play Obama presidential,' he said. "So all of the extra ticks that you could put in there, to give a view of his other side, were kind of stopped a little bit."

Under Mr. Biden, even the corporate comedy circuit has dried up. Denise Bella Vlasis, who runs the Tribute Productions agency in Los Angeles, explains, "People used to laugh at politics; now everyone is touchy. I've been in this business for 40 years, and I've never seen such a slump in interest in political entertainers."
Rich Little, a conservative who has told jokes about every president since Kennedy and is still at it at 84, has seen the shift. "There are a few people in my audience who are real lefties," he notes. "They just don't want anybody to make fun of Biden, no matter what."

Greg Gutfeld hosts a late-night show on Fox News Channel that is an island for conservative comedy. Example: "President Biden visited a Baskin-Robbins this week, making history as the first customer to get a brain freeze before eating the ice cream."

"Saturday Night Live," meanwhile, has largely abandoned presidential spoofs. The show has been in the forefront of such humor since 1974, when Chevy Chase anchored the first "Weekend Update" and coined a campaign slogan for Gerald Ford: "If he's so dumb, how come he's president?" During Joe Biden's first two years in office, he has been portrayed in only eight SNL sketches, while during Donald Trump's first two years the show satirized him 21 times.

I asked Al Franken, who helped write Mr. Chase's material and subsequently served as a Democratic U.S. senator from Minnesota, for his take on SNL's treatment of President Biden. "I think the reason for that is that they don't really have someone who does it well," he said. Ironically, the role was offered to Dana Carvey in 2019, but he turned it down because he wanted to avoid cross-country commuting.

Some comics who did go easy on Mr. Biden tell me they are not keen on him running for reelection. And the discovery of classified materials near the president's Corvette, has proved irresistible, prompting Jimmy Kimmel to ask, "Which is more dangerous? Joe Biden having classified documents in his garage—or Joe Biden having the keys to a Corvette?"

Lyndon Johnson decided not to seek reelection during the height of the Vietnam War, after comedians and journalists turned against him. LBJ is reported to have said, "If I've lost [Walter] Cronkite, I've lost Middle America."

What will Joe Biden do if he loses Colbert, Fallon and Kimmel?

(c) Peter Funt. This column originally appeared in The Wall Street Journal.