He won't be tasked to provide it, the state of Hawaii's Vital Statistics office will be. The head of the Health Department, of which Vital Statistics is a part, has already said they have "birth records". I doubt if she wants to be going to federal prison for contempt of court, or likely worse.
This is why the definition of “native born” is so important.
She has to have so many years in the US by such and such an age, and she’s the only one who has to be a US citizen.
IF they can establish her whereabouts prior to the birth, and if they can establish her whereabout following the birth, then the closer in time those are to the birth, then the more likely that Obama was born in the US.
She is in Washington State, I believe, one month after the birth and ready to go to college. They’re calling her residence a place under her parents name (lease?) prior to the birth. How likely is it that in that final month of pregnancy she disappeared to Kenya to have her baby, especially if they can establish his presence in the US at that time at some eastern college? The burden would be on those who would propose that, because travel wasn’t as easy in those days, and she would have been 8 months pregnant.
So, if they say that the original is lost, then they default to circumstantial and other evidence. At that point they would have to prove that Obama is NOT a “native born” citizen, and I’ve not yet seen the evidence that can do that.
Now, if someone rules that “natural born” IS NOT the equivalent of the “native born” law, then we have a different horse race, but I think that even then, his opponents would have to prove he was born outside the country, and the circumstantial evidence I know of doesn’t support that.
All that said, let me add that I’ve argued long and hard that he should release his original birth certificate, and that his obfuscation is insulting.
In that sense, I’m on the birther side. The most open presidency ever should be immediately open about all documents.