Stewart won't move onto anything bigger, he's already the biggest he can be. He gets better ratings then any show on any of the cable news networks, he can't take his show to network TV (too many toes to step on, no open slots available to give him), and I find it unlikely that he'll scale back his politics (like Colbert is apparently going to do) to get a higher profile gig elsewhere.
I guess he'll take some less demanding job eventually when he wants to. Maybe go back to doing standup, write a book, direct another good-but-not-great movie. Who knows, perhaps not even Stewart at this point.