From the Ark case:
"The foregoing considerations and authorities irresistibly lead us to these conclusions: the Fourteenth Amendment affirms the ancient and fundamental rule of citizenship by birth within the territory, in the allegiance and under the protection of the country, including all children here born of resident aliens, with the exceptions or qualifications (as old as the rule itself) of children of foreign sovereigns or their ministers, or born on foreign public ships, or of enemies within and during a hostile occupation of part of our territory, and with the single additional exception of children of members of the Indian tribes owing direct allegiance to their several tribes. The Amendment, in clear words and in manifest intent, includes the children born, within the territory of the United States, of all other persons, of whatever race or color, domiciled within the United States. Every citizen or subject of another country, while domiciled here, is within the allegiance and the protection, and consequently subject to the jurisdiction, of the United States."
All of the men who included themselves in the exception clause (the grandfather clause) in the Constitution were born on this continent, but their fathers were not American citizens. If what you are trying to float were definitive, there would appear to have been no need for the exception clause to be written into the Constitution.
Here's a piece of the puzzle copied from the Federalist Papers website:
Mr. Wong Kim Ark was born to parents who, though permanent residents of the U.S. when he was born, nevertheless remained subjects of the Emporer of China. In its decision in U.S. v. Wong Kim Ark, SCOTUS clearly articulated a broader scope of the 14th Amendment than had previously been recognized. In doing so, SCOTUS considered it important that Mr. Ark’s parents had demonstrated a clear attachment to the United States. In specifically recognizing Mr. Wong Kim Ark as a U.S. citizen (not a 'natural born citizen') under the 14th Amendment, SCOTUS laid down the general rule that any individual (other than children of foreign rulers and diplomats) born on U.S. soil to permanent resident alien parents is a citizen of the United States pursuant to the 14th Amendment.
Not satisfied with mere citizenship privileges for such individuals based on SCOTUS’s construction of the 14th Amendment, interlocutors now claim that this newly-recognized class of U.S. citizens must also be recognized as Article II, Section 1 “natural born citizens”, fully eligible to run for and assume the office of POTUS. But in order for SCOTUS to endorse such a theory, it will need to do so in a legitimate fashion, in a decision based on the results of an actual case or controversy brought before it, and taking into account all of the circumstances that gave rise to their positive citizenship decision for Mr. Wong Kim Ark, and not just some of them.
That is, if SCOTUS is to be called upon to loosen up the parental citizenship requirement on the one hand (so as to allow at least some individuals born to one or more non-citizen parents to assume the office of POTUS), it will need to hold these new members of the “natural born citizen” class to the special requirement that they be born to two permanent resident parents. Needless to say, and unfortunately for Mr. Obama, this is a result that does not necessarily accommodate individuals born to foreign fathers present in the United States on temporary student visas.
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And here is a quote from an actual court case where 'natural born citizen' is cited:
“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. For the purposes of this case, it is not necessary to solve these doubts. It is sufficient, for everything we have now to consider, that all children, born of citizen parents [PLURAL, 'parents'] within the jurisdiction, are themselves citizens.’ Minor v. Happersett (1874) 21 Wall. 162, 166-168.”