He could have all of the records moved to the National Archives. I do not believe he will go down easily and we already know that he does not feel constrained by the constitution much less, legalities or court orders.
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What would happen if he destroyed the evidence?
Sounds like a job for Sandy "Wide Cuffs" Berger. He is on a first name basis at the Archives.
Obama will declare that his Certificate of Live Birth is sufficient evidence, Game, Set, Match Obama.