Addressing Mr. Fallon again, he said, “Jared, I’ve sent you all around the world to represent me, but no one’s ever heard you speak. You’re like a little Jewish Amélie. Steve, you may be smart, but I once walked in on you eating a live pig in the Roosevelt Room.”

Mr. Baldwin said that whomever he did not pick would have to leave the Oval Office “and join Kellyanne Conway in the basement.” However, he said, that person “will get to come back at the end of all of this and help send me to prison.”

He revealed that he had chosen Mr. Kushner, and the Bannon character was taken away by another Grim Reaper. He called Mr. Kushner “an inspiration,” explaining, “You’ve shown everybody that if you’re born rich and marry my daughter, you can do anything you want.”

Instructing Mr. Fallon to “fix everything,” Mr. Baldwin sat himself at a smaller desk, next to the larger one he’d started at, where he and Mr. Fallon proclaimed the start of the show.

Later in the program, Melissa McCarthy (appearing by satellite from Los Angeles) reprised her recurring “S.N.L.” role as Mr. Spicer, the White House press secretary.

Mr. Spicer had drawn intense criticism over a news briefing on Tuesday in which he said that President Bashar al-Assad of Syria was worse than Hitler, “who didn’t even sink to using chemical weapons” (ignoring his use of gas chambers during the Holocaust), and then clarified his remarks to say, incorrectly, that Hitler “was not using the gas on his own people.”