The clause (if you really want to call it that....) does nothing more than authorize Congress to "define and punish ... Offences against" it.
Yet why give the general government that authority unless they were already bound by it?
The law of nature, when applied to states or political societies, receives a new name, that of the law of nations. This law, important in all states, is of peculiar importance in free ones. The States of America are certainly entitled to this dignified appellation.
James Wilson, Of the Law of Nations, Lectures on Law
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Further, it's pretty clear that the "Law of Nations" does not refer to any specific body of internationally promulgated law;
True. The Law of Nations is the basis FOR international law.
[From the above link:]
The opinions of many concerning the law of nations have been very vague and unsatisfactory; and if such have been the opinions, we have little reason to be surprised, that the conduct of nations has too often been diametrically opposite to the law, by which it ought to have been regulated.
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It is, further, quite clear that the context of the term as used in the clause you cite is much different from any questions of Obama's citizenship.
Congress has no authority to decide who will or will not be a citizen, that is determined by the circumstances of a person's birth. The Law of Nations is the guideline Congress must follow when that birth occurs. The father's citizenship determines the citizenship of the child, and Obama's father was not a US citizen.
Why is the term 'natural-born citizen' so hard for people to understand?
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James Wilson argued in 1774 that the American colonies should be free from the rule of British lawmakers in his widely read Considerations on the Nature and Extent of the Legislative Authority of the British Parliament. His writing soon led to involvement in the planning for American independence. He represented Pennsylvania at the Continental Congress from 1775 to 1776, and 1782 to 1783, and signed the Declaration of Independence in 1776.
He later became an associate justice on the US Supreme Court, and, in the same year, was made the first law professor of the University of Pennsylvania.
With all due respect, I'll take Justice James Wilson's opinion over yours.
Again, you have to consider that "the law of nations" is more a philosophical position -- a generally accepted sense, shareed among nations, of what is right and wrong. But as the FindLaw discussion points out, the practical aspects of that position were not precise. Probably the best (relatively) recent example would be the Nuremburg trials following WWII. It was quite clear that real crimes had been committed by the Nazis, althoug there was no established body of international law that actually codified those crimes. In that case, the general sense of "criminal activity" would have been justified by the "law of nations."
Congress has no authority to decide who will or will not be a citizen, that is determined by the circumstances of a person's birth.
That's a false assertion. In the present context, Congress passed the law governing the definition of a U.S. citizen, as codified at USC 8.1401.