I like this quote right here:
At common-law, with the nomenclature of which the framers of the Constitution were familiar, it was never doubted that all children born in a country of parents who were its citizens became themselves, upon their birth, citizens also. These were natives, or natural-born citizens, as distinguished from aliens or foreigners. Some authorities go further and include as citizens children born within the jurisdiction without reference to the citizenship of their parents. As to this class there have been doubts, but never as to the first.
- Morrison Waite 1875
Some authorities go further and include as citizens children born within the jurisdiction without reference to the citizenship of their parents. As to this class there have been doubts, but never as to the first.
I'd like to point out two things. First, the "have been doubts" is a reference to citizenship at all, meaning that there are doubts that all (non-diplomatic) persons born on the soil are even citizens. Second, the framers of the constitution would not have used a term that they thought admitted doubts. Obviously, they could not have predicted that the constitution would include a right to abortion or homosexual marriage, and other subversions that have become common, but there is no way they would have deliberately selected a term of art that was obscure or ambiguous.
Heck, they knew that they, citizens themselves, were naturalized by the creation of the country - and they didn't go through a "naturalization procedure" either!