I don't think Dean would have been able to beat Bush. It's very difficult to defeat an incumbent and by 2004, Iraq was still a fairly popular war nationally (the bottom hadn't fallen out like it would in '06) and the economy was showing some signs of improvement (after it struggled in Bush's first three years).
The fact Kerry, who was fairly moderate an even-tempered, couldn't beat Bush, though he did come close, probably suggests not only would Dean lose, but he would lose badly.
I don't think it would be a McGovern-like landslide (hard to imagine Kerry changes the EC THAT much), but it would not have come down to one state like it did in both Bush's election wins.
Dean would have rallied the left, struggled with moderates, but his anti-war message, at a time when Americans weren't necessarily opposed to the war, but the way it was being handled, would have led to a map like this:
Dean: 185
Bush: 353
Just my guess, though. I think Dean would have failed to win a state Kerry lost, though, I guess, since Vermont was a neighbor to NH that it's possible he wins there (and might play better in, say, Colorado & New Mexico). But still, if I had to guess, I say he loses Wisconsin (Kerry narrowly won it), New Hampshire, Michigan (Kerry narrowly won it), Pennsylvania and New Jersey.
But who knows.
For full disclosure, even though I wasn't of voting age back in '04, I worked and supported Dean's campaign. So, no hate for the governor, I just think it would have been very difficult to win (any Democrat, really, would have struggled to beat Bush in '04 - just as the Republicans will struck to beat Obama in '12 - it's the nature of the game).