Jon Stewart. (Astrid Riecken/FOR THE WASHINGTON POST)

After Fox show host O’Reilly pointed out that Stewart had criticized President Obama on “The Daily Show,” he took it a step forward and asked the liberal host if he’d vote for a Republican candidate for president. “Sure,” Stewart said, qualifying what Obama would have to do to lose his vote: “If I didn’t have a clear sense of the direction that he wanted to move the country and somebody else had a more logical sense of where to take it.”

So what potential GOP candidates would Stewart vote for? Tim Pawlenty and Mitt Romney would be “viable candidates” because they were both decent governors, Stewart said. But former governor Sarah Palin? Not so much.

“I'm not a particular fan of her style of rhetoric. I think she's too thin-skinned,” Stewart told O’Reilly, who said the description sounded more like Stephen Colbert. “Colbert, I would actually endorse for president,” Stewart joked. “She's reminiscent to me much more of a television personality than a politician because I think that her inability to get past slights,” Stewart added of Palin.

But Stewart said he “prays” businessman Donald Trump runs, even though the businessman announced he wouldn’t seek office earlier this week. Stewart echoed this plea on Tuesday night’s “Daily Show.”

When O’Reilly asked if Stewart takes Trump or any potential candidates seriously, he didn’t say no but gave an answer to that effect. “Because I think, you know, unfortunately the system that we've got makes it harder and harder for people to govern effectively because so much of their time is spent running,” Stewart said. And you know what? O’Reilly agreed with that. It seems these two media figures could find common ground after all.