It's hard to say. You can make a case either way.
The argument that the birthers' lies hurt Obama is the more obvious of the two. The more credence given the lie of Obama's foreign birth (a poll shows that 45% of Republicans believe this untruth), the fewer Republicans and Independents are available for conversion to Obama's brand of fence-walking. The more voters are preoccupied with Obama's citizenship papers, the less they follow policy arguments in which Obama and the Democrats hold a public opinion advantage over Republicans (e.g., not privatizing Medicare, exacting more taxes from the rich). From this point of view, Obama's throwing up his hands and waving his birth certificate at a televised press appearance was a cave-in to the manufactured legitimacy of the birthers' empty rants, a way of crying Uncle and declaring to a playroom full of six-year-olds, "Awright, dammit, I'll PROVE to you that there's no Santa Claus!" Once an important man lowers himself to refuting lies that deserve no attention, the lies win -- by gaining weight via the import of his attention. He won't change any minds; he'll just raise the profile of the lunatic fringe.
But there is an opposite argument to be made, too: namely that the birther nonsense has beautifully divided the Republican Party in a way that Dems never could. The more the ridiculous Donald Trump -- with his comical blond comb-over -- revs up the yahoos with his stand-up lie routine about Obama and a host of other subjects, the more of a joke the Republican Party becomes to voters who have more than two brain cells to rub together. The more the Michele Bachmanns and Scott Warners and Sarah Palins crawl on all fours in stances that would make a lemur feel embarrassed to be a primate, the more the Republican leadership pulls away from its pre-human base. From this standpoint, the birthers' insistence on miring themselves in a freakishly absurd issue is an astoundingly generous gift to Democrats. Like Senator Paul Ryan's plan to deliver Medicare into the greedy hands of the private sector, it forces Republican politicians to choose between a raving hard-right voting bloc and the good sense of a healthy proportion of Americans. And Obama's grownup chastising of the weak-minded kiddie crazies in the electorate highlights the contrast between Republican loonies and the remainder of the G.O.P. Savvy Democrats might very well want to shout, "Go, Trump, go! You tell 'em, Don!"
If I thought I knew which way this is going, I'd say so. But I don't. So I'm watching.