Interesting question. I've often wondered about that myself.

I think the real significance of Stewart and Colbert is that there one of the only places on television (the other to some extent would be MSNBC) where unabashedly progressive political voices are tolerated -and they only get away with it by dressing it up as comedy -and by bringing in truckloads of advertising $$$ for the Comedy Network. As with right wing talk radio or Fox News I have no doubt this is mostly a "preaching to the converted" phenomenon, in that their audiences are mostly young people who are already favourably disposed to their politics, but in an era of high anxiety about the alleged political disengagement of youth (which I think is often seriously overstated anyway) they play an important role in framing political issues in a way that makes them accessible to viewers. Some of Stewart's interviews with right wing figures have been absolutely devastating. He basically got Crossfire cancelled on CNN after he appeared on the show as in the interviewee and ridiculed the show's lack of substance and serious debate. I think Stewart is under some pressure from the network to moderate the show's tone however. Lately his experimented with a "pox on both your houses" approach, most lamentably in the "Rally to Restore Sanity", in which he lampoons the broken political system itself, for which both parties are held responsible, rather than specific (and mostly Republican) policies. I imagine it's quite a tightrope act trying to please his corporate overlords while not alienating his audience!

I think I've become more of a fan of Colbert for that reason. Plus Colbert has better guests. Stewart's guest list is heavily slanted toward Hollywood celebrities promoting their latest big studio release, which hardly seems appropriate for a faux news show. Isn't that what Letterman and Leno are supposed to be for?

Very.
Humor is persuasive; it's an equalizer. Laughing at a politician/candidate/policy/international relationship/billionaire/pop-culture maker chips away at the pedestal. 

Granted, there are lots of kinds of power...and I don't know which Stewart's is, really. How do we measure a pundit's power? 

Regardless, I think he's changed how many people view politics and the political process, and that change is important in its own right.

Stewart's defense of his own politics is that he is first and foremost a comedian. His program is on Comedy Central and was contracted to make audiences laugh not think.

The Daily Show is definitely not real journalism or punditry and it's dangerous to consider it such. However, when compared to the paltry state of popular news media today, The Daily Show genuinely holds up by using a simple model of practiced journalism: compare and contrast. 

The Daily Show most holds up alongside 'real' journalism when it exposes both media and politics as constantly shifting and unstable platforms for truth. 'Look at what this politician says here. Now look what he says 5 months later.' By pigeon-holing himself into a strict corner of comedy Stewart wonderfully avoids the hypocrisy that beleagues traditional forms of journalism and politics. Accordingly, Stewart's power (different I think from Colbert's) is  his ability to disengage his audience from their faith in his subject matter (politics/media).

I think Emma is correct in saying Stewart preaches to the converted in that his audience is mostly young and liberal. However, I do not think this is what prevents Stewart from being genuinely powerful among his demographic, moreso I think it is that his coverage alienates his audience from politics and government and media without providing an alternative except laughter. Of course, laughter is good enough by itself, but when Stewart goes so far as to lead a Washington D.C. rally during election season, he should have had the gall to attach a better political message to it than "Beck is an idiot. If he can do it so can I."

Were Stewart to have a go at harnessing his own power he would need to make a claim. As of now, his show is mostly passive. It's most exciting to watch when he takes on face-to-face right wingers and throws hypocrisy from across the table. But to do that full-time is probably something he isn't interested in, knowing full-well that laughing at your own stance is harder than picking apart other people's.