Jon Steward would bring quite a few viewers with him! He is funny, political, and he isn't shy about talking about things that are important. I think they would keep their current viewers and then he would bring along all of his viewers and that they would have quite a few people watching.
If Jon Stewart were to host the Meet The Press, I imagine that the curiosity factor would spike initial rating. However the question is how long would he retain those new eyes once the novelty wears off? If he can balance that fine line between his humor and incisiveness without scaring potential guest away, I imagine he can hold to a good portion of them.
Jon Stewart is certainly a lot more popular than anyone else on Meet the Press. Initially viewership would skyrocket due to his fans and curiousity seekers. However after time, I think the ratings would fall back a bit toward the current norm. Nevertheless the ratings would still be higher than they are now.
I'm not impressed with Jon Stewart and his show on Comedy Central, which appeals to the lowest common denominator. He's a yuck-yuck man through and through proving you can make a career out of being the class clown. Politically, he is your typical leftist hack and a self-hating Jew to boot. It only serves to demonstrate that NBC executives are looking for the right political attitudes and ultimately they will continue in their decline.
While pursuing Jon Stewart may have seemed like a good idea in theory for NBC executives, in reality it would not have worked out the way they would have liked. Stewart's fan base tend to be young night owls. That's why the night time slot at Comedy Central has worked so well for him. I would guess that many in his primary demographic have never even heard of Meet the Press, let alone seen it. A Sunday morning time slot is maybe the worst possible time slot for this group. On the other hand, Meet the Press's current viewers would probably be less than impressed by Stewart.