Let's examine this.
First, one should understand the entire issue of "birtherism" has nothing to do with where Obama was or wasn't born. It has nothing to do with eligibilty to be President. It has everything to with Obama's skin color and that he has a foreign-sounding name.
Second, producing this birth certificate or any other evidence will do nothing to change the fact of Obama's skin color and name. Birthers are not going to go, "well, I was wrong and now I support the President."
Not gonna happen.
Third, Obama producing this birth certificate was a tactical and strategic blunder. Here's why: the only people who are "birthers" are extreme wingnuts/Tea Party cranks. There is nothing Obama could do to sway these folks--so why bother? OTOH, moderates and independents tend to view "birtherism" with the same jaundiced eye as Big Foot sightings and the Hale-Bopp cult. Thus, every time a GOP politico or candidate is asked about "birtherism," they face a very uncomfortable situation. They can align themselves with the TeaParty/tinfoil hat crowd and risk losing moderates and indpendents or they could renounce bitherism and lose the TeaParty extremists or they could try to weasel out of the question and piss off everyone.
IOW, birtherism hurts the GOP and presents them with a "no-win" situation. Rove and a number of GOP strategists understand this; in fact, Rove so hates the issue, he has accused Obama of creating it.
Further, if I'm a Dem strategist, I *want* fringe kooks like Trump and Bachmann and other birther candidates out there sucking oxygen and air-time away from more moderate GOP candidates. I *want* these folks out there as the 'face' of the GOP. Why on earth would Obama want to stop this circular firing squad?
Re Trump: liberals need not worry about him. In fact, we should encourage his candidacy. Why? First, he's not going to run; he's done this twice before. He does this for free publicity. The first time he ran for Prez he was promoting his first book. This time, he's using a phony run to keep his TV show's numbers up. Second, the longer he remains a GOP frontrunner helps Dems because it points out exactly how weak and useless the real GOP field is.
Who on earth thinks Trump will actually run? I don't think the Donald is the brightest bulb out there but I give him credit for not being completely retarded. Does anyone think Trump wants his finances scrutinized? His personal life? He's already shown that when he moves off issues unrelated to birtherism, he's way out of his league. No, the Donald loves the publicity but he doesn't want the job.