I have my own take on the "birther" conspiracy hysteria that has sprung back into the spotlight with the media-whoring binge that Donald Trump has been on lately. I believe that it is entirely possible that Obama himself, or one of his staff, came up with the idea to draw out the people that hated him the most. Give them something absurd to put all of their energy and attention into which is the easiest thing for the intellectually lazy, then use that as a trap to discredit anything else they would possibly want to oppose Obama with.
Even if it wasn't his idea originally, he is certainly using it to his advantage and will continue to use it. It's a very savvy move.