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Jon Stewart hasn’t been obnoxious about it, but he has shrewdly used his platform hosting “The Daily Show” to promote his directorial debut, “Rosewater,” in advance of its Nov. 14 opening. That’s no surprise, given that his name is essentially the marquee draw on this passion project.

And that should give the folks at Comedy Central, who have seen a version of this movie before, a slightly uneasy feeling, wondering how they can keep their foremost star happy if Stewart decides — in true Hollywood fashion — that what he really wants to do is direct.

Stewart has been all over the place discussing the film — good luck looking for outlets that haven’t interviewed him — and he’s acknowledged both that his contract is up next year and he isn’t sure about extending his 15-year run as host. While there’s the tantalizing prospect of staying at least through the 2016 election cycle — talk about a target-rich comedic environment — Stewart has sounded like a guy enthused about his creative muscle-flexing and grappling with a bit of fatigue.

For Comedy Central, losing Stewart — whose cultural influence can’t be measured strictly in ratings or revenue — would be enough of a blow on its own. Yet it would also come on the heels of his companion Stephen Colbert leaving for CBS, and in perhaps the biggest indignity, John Oliver capitalizing on his stint filling in while Stewart was off directing the movie to launch what amounts to a weekly version of the program at HBO.

That’s a lot of brain drain to weather, even if “The Daily Show” has demonstrated its ability to cultivate new talent. Simply put, the list of people who can successfully front a latenight franchise remains relatively short, and Stewart’s ability to straddle the lines separating entertainment and politics have made his voice echo louder than most.

In what amounted to a finishing kick, Stewart devoted his entire program on Thursday to plugging “Rosewater,” even enlisting Oliver to stand in (again) as host, interviewing journalist Maziar Bahari; the actor who plays him, Gael Garcia Bernal; and “Daily Show” correspondent Jason Jones and his producer, whose 2009 visit to Iran set in motion the events that resulted in Bahari’s imprisonment and torture. Even the commercial pod contained — what else? — another ad for the movie.

Although the host has seemed slightly embarrassed about engaging in self-promotion, it’s hard to remember an on-air talent doing more to tout a film with which he’s involved since Howard Stern’s build-up via his then-syndicated radio show to the release of “Private Parts.”

Asked about his plans to direct again Stewart has been largely coy, telling CNN, for example, that the decision doesn’t entirely rest with him. Yet given the generally favorable reviews that have greeted the movie, it’s not far-fetched to think there would be additional opportunities, even if the box office results are modest.

It’s a little premature, obviously, for anyone to start panicking. But if Comedy Central isn’t feeling a tad nervous about this weekend and its potential implications in regard to Stewart’s future, then somebody might be viewing the situation through rose-colored glasses.

This post has been updated to include the Nov. 13 edition of “The Daily Show.”