Isn't it possible that the Constitutional Convention's final Committee of Style agreed upon a specific definition for the "natural born citizen" term ....? I have three competing theories on this.
1. Yes they did. They were all in exact agreement as to the meaning of the term.
Corollary a. It was based on Vattel.
Corolllary b. It was based on English Common law.
2. There was no uniform understanding of the term, but everyone believed the others thought exactly like themselves, though there must have been a majority on one side.
3. In actual practice, the English Law theory closely followed the Vattel definition. Alien born children in England may have been called "subjects" but they had very different standards of acceptance within English society than did Subjects born to English Parents. Here is a law passed by William III.
Note the reference to ENGLISH PARENTS being required to hold public office?
The English simply did not grant the same class of citizenship to those born of Alien Parents as those born to English Parents.
I have only one thing to say to you:
"Les naturels, ou indigines, sont ceux qui sont nés dans le pays, de parents citoyens."
Actually, I've read enough of this baloney to agree with you that there were some very important people back then who apparently looked to Vattel for guidance regarding theories of citizenship. But, I also know that many of these guys were lawyers of great ability with years of drafting experience. So, I know that:
When these guys wanted to avoid ambiguity or uncertainty, they knew how to do so.
When, instead, they wanted to delegate some discretion (wiggle) room to future decision makers, they knew how to do that, too.
The kind of fellow who had heard of Vattel and who was actually reading Vattel knew enough about politicians to know that, if it was felt to be really important to strictly bind future politicians (electors) to a definition as precise as native birth to two citizen parents, then it would be important and necessary to draft appropriately precise and binding instructions. Whether by intention or inadvertence, the Constitution includes a term without contours or boundaries as specific as Vattel might have prescribed. I think it would be unfair to the ordinary citizen of that time to just assume that any one precise definition of natural born citizen would have been obvious or commonplace.
Obviously, there are two competing interests at stake here. The first is that we want a president who is "one of us" in that he or she has a close connection to the country by heritage and by experience. The second is that we don't want to limit our pool of candidates any more than is really necessary. I think that the Constitution provides electors with some discretion in striking an appropriate balance between these competing interests.
I think the Constitution affords to this generation the liberty to choose Ted Cruz, a citizen at birth, as our president. I'm confident that if the public perceives that either his birthplace or his father presents a substantial danger, the public will simply choose someone else.