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What's interesting is what Vattel himself says in section 214 (http://www.constitution.org/vattel/vattel_01.htm):

§ 214. Naturalization.(58)

A nation, or the sovereign who represents it, may grant to a foreigner the quality of citizen, by admitting him into the body of the political society. This is called naturalization. There are some states in which the sovereign cannot grant to a foreigner all the rights of citizens, — for example, that of holding public offices — and where, consequently, he has the power of granting only an imperfect naturalization. It is here a regulation of the fundamental law, which limits the power of the prince. In other states, as in England and Poland, the prince cannot naturalize a single person, without the concurrence of the nation, represented by its deputies. Finally, there are states, as, for instance, England, where the single circumstance of being born in the country naturalizes the children of a foreigner.

Note that the bold sentence refers to England, whose laws on citizenship were used in the colonies. Thus, Vattel is clearly admitting the English practice as entirely valid and is no way insisting that the new United States of America was obligated to adopt any other manner of declaring who was a citizen at birth than that already in use.

Thus, Vattel is clearly admitting the English practice as entirely valid and is no way insisting that the new United States of America was obligated to adopt any other manner of declaring who was a citizen at birth than that already in use.

Sure, naturalized at birth is a possibility, though it does not equal natural born. We might as well throw in the next section, too:

§ 215. Children of citizens born in a foreign country. It is asked whether the children born of citizens in a foreign country are citizens? The laws have decided this question in several countries, and their regulations must be followed.(59) By the law of nature alone, children follow the condition of their fathers, and enter into all their rights (§ 212); the place of birth produces no change in this particular, and cannot, of itself, furnish any reason for taking from a child what nature has given him; I say "of itself," for, civil or political laws may, for particular reasons, ordain otherwise. But I suppose that the father has not entirely quitted his country in order to settle elsewhere. If he has fixed his abode in a foreign country, he is become a member of another society, at least as a perpetual inhabitant; and his children will be members of it also.

So, applying §214 to Obama, he could be naturalized by the U.S. However, according to §215, British law would also make a claim on Obama Jr. as a child of a citizen born in a foreign country, of which Vattel says "their regulations must be followed". If both the U.S and Great Britain are applying the same law, then the Obama could have naturalized at birth, but he was still, legally, a British subject.

Sounds like a turf war; I say we concede this round and let the Queen keep him ;-)