Very interesting argument. I'm curious to see if there were ever writings from the founders on this subject; I can see why they would have wanted to temper any potential foreign influence in a fledgling nation, especially one that came to be as America did. I doubt they exist or I probably would have heard about it amidst the birther movements, but that still leaves the central mystery regarding what "natural-born" means. If the Supreme Court weighs in, I would wager they'll take the more liberal interpretation.
Food for thought, though. If the child of illegal immigrants becomes a contender for the office in a few decades, it will be very interesting to see how that is resolved.
I would certainly hope that we clear up that issue before we are faced with it, but we very likely won't address it proactively. I don't understand the anchor baby concept anyway for illegal aliens. It should follow the fruit of the poison tree logic - their being here illegally should void US citizenship for the children. It's gaining something positive from an illegal act, and the kids still have Mexican or whatever nationality; they aren't stateless like the supporters would want you to believe. Otherwise, Cruz wouldn't have US citizenship regardless of his mother's status. That in itself should discourage the illegal invasion.
Emerich de Vattel wrote The Law of Nations, in 1758; it includes this passage:
The citizens are the members of the civil society; bound to this society by certain duties, and subject to its authority, they equally participate in its advantages. The natives, or natural-born citizens, are those born in the country, of parents who are citizens. As the society cannot exist and perpetuate itself otherwise than by the children of the citizens, those children naturally follow the condition of their fathers, and succeed to all their rights. The society is supposed to desire this, in consequence of what it owes to its own preservation; and it is presumed, as matter of course, that each citizen, on entering into society, reserves to his children the right of becoming members of it. The country of the fathers is therefore that of the children; and these become true citizens merely by their tacit consent. We shall soon see whether, on their coming to the years of discretion, they may renounce their right, and what they owe to the society in which they were born. I say, that, in order to be of the country, it is necessary that a person be born of a father who is a citizen; for, if he is born there of a foreigner, it will be only the place of his birth, and not his country.
Probably some of our early statesmen and founders would have been familiar with that. The interesting part is that he starts with parents who are citizens and then somehow ends with "father who is a citizen." Following either thought would have precluded Cruz and Obama as president. These days we just always seem to make the rules on the fly when confronted with a problem rather than through real deliberation. Sometimes simple bluster and failure to act wins the day.