Is there any advantage for Obama to not produce the required document(s) NOW?
It doesn't take a legal mind. I think he probably is a US citizen but there is something embarassing on his birth certificate. There are many possibilities.
My theory is that his real BC shows his father's race to be ARAB. Obama's father was only fractionally black, he was 87.5% Arab and 12.5% black (which is why he has an Arab name). That makes Obama only 6% black, 43% Arab and 50% white. By US definitions therefore he is not black, he's under the legal threshhold. For example this means Obama was lying when he called himself the first Black president of the harvard law review.
Now before anyone calls me a racist for pointing this out, I will retort that a couple of million black people in the USA are clearly voting for Obama precisely because they believe he is black. IF it turns out he is really an Arab legally, he may well lose many of their votes. If his birth certificate makes it clear his father was an Arab, that could be game, set, match.
All I know is that Obama's father is one of the blackest men I've ever seen (a picture of.)