As Hurricane Florence headed toward the Eastern Seaboard in September, Ted Tremper, the showrunner for “This Week at the Comedy Cellar,” realized he had a problem, and it wasn’t damage from the storm. He needed jokes.

It was the final day of shooting for the test show, and while he had hours of footage of comics weighing in on eight categories (Trump, #MeToo, Colin Kaepernick, etc.), he had no punch lines about Florence.

As a former producer of “The Daily Show With Trevor Noah,” he knew humorous takes on the news needed to stay current. But there was another issue. Some forecasts were suggesting Florence could be catastrophic. As Tremper explained before the first sets of the night, “The challenge is: How do we comment on this without doing a joke in poor taste?”

That’s probably not the last time he will have to answer the question of how to successfully shift the context of jokes from the Comedy Cellar, the premier club in New York, to national television. The new show, which made its debut Friday night on Comedy Central, arrives at a critical moment for the Cellar, which has become the subject of controversy just as it tries to expand its empire.