I'm not sure most of the people who are harping on this "birth certificate" issue even believe it's true; I think they're mostly looking for something to badger the winner with. It's amazing what people will do when they're feeling bitter.
Are there racists among them? I assume so, but I'm not sure what fraction it is, let alone if it's the majority. As for the rest of them, logic isn't at issue with most in this situation. It's an emotional response, just as many reactions are in the political arena. There were nut-cases dogging every President in recent memory, forcing them to spend time and attention on trivia - taking their time and energy away from the larger problems facing the people of this country.
Many of them, in this case, have trouble feeling any sort of sense of commonality - or community - with the duly elected former Senator for any number of reasons: some because he's not white, some because he's a Democrat, some because they think he's trying to impose socialized medicine, some simply because they thought we were doing well under the previous administration.
Right or wrong isn't at issue - logic won't change their position; they aren't open to debate, they aren't even listening. Sadly, it's the same sort of "we vs. they" thinking that is so easy to see as problematic in places like the middle east, but when we're caught up in it ourselves we lose our objectivity. It's great in a game of bridge, or as a fan at a sporting event, but inappropriate and counterproductive in this case.
So they pick something to hammer away at, something that doesn't sound - on the surface - like they can't abide a Democrat, or a man who's not another good ol' white guy, or whatever their particular thing is, in the White House. It's a mantle of plausible deniability, distancing their words from their true objection. As such, they're no more objective, or amenable to logical discussion of facts, than the Emperor in the parable that teaches us (or at least tries to) about keeping our perspective.
It doesn't take mental illness, or racism, to account for what's going on. All one of these conspiracy theorists needs is to be a little bit stubborn: pleased to believe that you can't call them anti-black, or anti-Democrat, while they hide behind the story that there's something suspect about a guy who beat out their guy.
In due time some will realize, like the emperor with the "new" clothes, that they've not got even one scrap of evidence to hide behind.
Some few may even expand their view, and decide our President is a lot more like them despite having parents of different colors, and a lot more interested in their welfare than, for instance, a Saudi prince.
But the man's only been in office about 7 months, and that's not a lot of time to win over the opposition while he's busy trying to dig us out of the hole the economy fell into during 2008. He's adopted an ambitious agenda: health care reform alone would be a major task, but he's working international diplomacy, education, and climate reform as well. He's got supporters who think he's not moving fast enough on their own top priority, be it civil rights for gay couples or reforming and regulating Wall Street.
The extreme cases, of course, will remain unswayed no matter how much success Obama has. Like extremists for other points of view elsewhere, they will make a lot of noise because they crave the attention more than anything.