I'd like to become President. Although I am a UK FReeper, what you are saying is that the onus is on YOU to prove I wasn't born in America. I can just claim citizenship.
What's that? You'd like me to present my Birth Certificate? Umm, look, I put a photo-shopped fake up on my presidential website. Isn't that good enough for you?
For the purpose of establishing basic qualifications for holding elective office, the historic burden of proof in the US has always been on those trying to disprove a candidate’s qualifications. That means you have to prove that he’s not a natural born citizen, which I don’t think is even remotely possible.