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Absurd! Are you honestly willing to go that far to defend your belief that BHO II isn't eligible to be POTUS?
What is the "law of nations," anyway? Perhaps if we describe it differently, it will become clear: public international law (i.e. FOREIGN law).
Justice Scalia has made it clear that he "[does] not use foreign law in the interpretation of the United States Constitution."
You can call it "natural law" or the "law of nations" all you like, but at the end of the day, you're using "public INTERNATIONAL law," and that makes you closer to Justice Breyer than Justice Scalia. That doesn't make you wrong, but it does mean you're no longer a conservative.
Common law is case law, end of story. If you want to say that the "common law" Chief Justice Waite mentioned in Minor isn't English common law, fine. Provide a case between 1776 and 1788 showing that we moved away from the English common law definition of "natural-born subject" to de Vattel's "les naturels."