I very much doubt if Jon Stewart, in his personal self, is Republican or conservative. But I suspect that his show has made him a sort of secret weapon for Republicans in the South. Stewart loves to make fun of those quaint and silly Southernisms of guys like Lindsay Graham and Mitch McConnell. I figure that every time he does that, he gets them about a 2% uptick in their vote.
A lot of the Southern vote has always hinged on famously wounded Southern pride, and hearing that sort of thing from a liberal New York Jew has got to sting. It's not really that funny either, and Graham and McConnell offer lots of more substantive satirical targets - targets that don't rely on cheap ethnic humor.