On the rare occasions that Barack Obama’s name is so much as mentioned, he receives gentle, if not admiring, treatment.

And so it only seemed to confirm the existing suspicions of political observers that the writers and actors of SNL harbor a soft spot for the underdog senator from Illinois when, this weekend, Mr. Obama himself made an unexpected debut appearance and delivered on-message lines in the show’s opening sketch.

“You know, Hillary,” Mr. Obama said to the Hillary character, played (brutally) by Amy Poehler. “I have nothing to hide. I enjoy being myself. I’m not going to change who I am just because it’s Halloween.”

But according to the show’s top producers and writers, Obama isn’t getting a pass because the cast actually supports him. It’s just that there’s not enough there yet to make fun of.

“Not yet,” said Lorne Michaels, the show’s longtime executive producer, in a phone interview. “I think he is still an ingénue.”

Mr. Michaels believes that Mr. Obama has so far failed to tap into the American consciousness, and therefore he lacks the necessary resonance to be funny.

“He is not as defined to our audience as he is to political reporters,” said Mr. Michaels.

So the good news for Mr. Obama is that he’ll continue to be spared the rough treatment Mrs. Clinton has been subject to.

The bad news is that with just weeks to go before the first votes are cast, he’s struggling to achieve traction not only in the national polls, but on the national comedy circuit as well.

Some of the show’s top writers, picketing outside Rockefeller Center on the afternoon of Nov. 5 in support of a freshly declared writers’ strike, explained that Mr. Obama’s absence from the program was due first and foremost to the fact that no one had figured out how to play him or what was funny about him.

“It’s not a pro-Obama thing,” said Steve Higgins, a 44-year-old writer and producer of the show.

He said that the writers seemed pretty evenly supportive of—or indifferent to—Mrs. Clinton and Mr. Obama. The difference, he said, was logistical. While one of the show’s stars, Ms. Poehler, was physically suited to play Mrs. Clinton and had developed her own take on the character, no actor or story line seemed obvious for Mr. Obama. The show’s only black male cast member, Kenan Thompson, is short and fat.

(“The SNL cast didn’t have anyone that tall and skinny, so they asked him to play himself,” said Obama spokeswoman Jen Psaki, by way of explaining the appearance.)

Mr. Higgins did say that Maya Rudolph, daughter of the late African-American soul singer Minnie Riperton and Jewish-American composer Richard Rudolph, was working on an Obama impression. She already has impressions of Halle Berry, Liza Minelli and Whitney Houston on her résumé. But Mr. Higgins said she had so far failed to nail down her Obama.

And even that wouldn’t be guaranteed to solve the problem.

“Even if there was an actor to play him, the writers are having a tough time,” said Mr. Higgins “The story line is the anointed one who is no longer anointed.”

He then made the face of someone bored out of his mind.

“It’s like he’s up against a steamroller and he’s done as well as he can,” he said. “What’s funny about that?” Mr. Higgins also said that the senior writers and producers are all open to Obama pitches, but there had been a shortage of jokes promising enough to air.

For Mr. Obama’s appearance, the SNL staff proposed several possible sketches, but he declined to participate in most of them. One proposed skit, according to Mr. Higgins, was for the “Weekend Update” segment of the show, in which Mr. Obama was asked to deliver an O.J. Simpson–esque “If I would have beaten up on Hillary” speech.

(The campaign wisely turned it down.)

Interestingly, it’s Mrs. Clinton—who is often portrayed as having an almost Nixonian lack of humor—who might most benefit from a “sock it to me” appearance on the show.

Indeed, in addressing the idea of a pro-Obama bias on the show, Mr. Michaels pointed out that the Clinton campaign had in fact tried to arrange an appearance for the season premiere, but that it fell through because of scheduling conflicts.

“If she had come on, everyone would have said we were tilting towards her,” said Mr. Michaels.

Watching the show, though, no one could make that mistake.

In a skit that aired before Mrs. Clinton officially declared her candidacy, the Hillary character tells an interviewer, “Is there anyone in the f-----g country who didn’t know I was running for president? I’ve been running for president since I was five! Are you f-----g retarded?”

And at one point in the most recent show, she tells a John Edwards character that, come next November, “we all have to support the Democratic nominee. No matter who she may be.”

“She is a richer character,” explained Colin Jost, a 25-year-old writer on the show who was also out picketing on Monday afternoon. “You can do a million things with her. There’s more history with her that you can pull from.”

Mr. Michaels went so far as to suggest that Ms. Poehler’s Hillary impersonation had a benign undertone.

“There is an attitude that she is playing that I find kind of sympathetic,” said Mr. Michaels. “The thing with Bill is kind of like—bemused.”

During Saturday’s opening sketch of a Halloween party thrown by the Clintons for Democratic presidential candidates, the Hillary character, in costume as a bride, is repeatedly mistaken for a witch. Her caddish husband Bill, who was supposed to have dressed as the groom, arrived instead dressed as Mystery, from the VH1 reality show The Pick-Up Artist.

The last guest at the party arrives in an Obama mask, which is removed to reveal Mr. Obama himself. Looking a little wooden but getting a huge hand, he says to the Hillary character, “May I say, you make a lovely bride.” Whereupon the Bill Clinton character interjects, “She’s a witch.”

“The witch was just playful,” said Mr. Michaels, who described the costume as a metaphor. “Whatever her costume is, she is just perceived by one group of people one way and by another group of people another way.”

According to John Solomon, a 37-year-old writer on the show, the sketch “mirrors Americans’ perception” of the race. Which is, in the end, not such a ringing endorsement of Mr. Obama.

“You can try and get them to like somebody they don’t like, but it is not going to happen,” said Mr. Michaels. He added that an Obama character would appear when the country had a better sense of the candidate. “The more that he starts to wear and people say, ‘That’s who he is,’ and have a clearer sense of it—that’s good.”