Unfortunately, there are no SCOTUS cases, to the best of my knowledge, which discuss the definition of "natural born citizen" as related to presidential qualifications. Some scholars contend that it means "born of US citizens," others that it means "born on U.S. soil," and still others that it means that both of these criteria have to be satisfied.
“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 indigenes are those born in the country of parents who are citizens. Society not being able to subsist and to perpetuate itself but by the children of the citizens, those children naturally follow the condition of their fathers, and succeed to all their rights.” (natives and indigenes mean Marshall was refering to the French edition of Vattel; subsequent English translations used natural-born citizen - citizenship defined by nature and not by law.)
Then, if you are really interested, try Minor v. Happersett and Wong Kim Ark and Perkins v. Elg. There is even a case from 2001 in which the citizenship of parents is discussed with an uninformed Justice Ginsberg, but the full statement not repeated - just citizen parents, which alarmed her because her grandchildren were born in France and would not be eligible for president.
Then read John Bingham, co-author of the 14th amendment, speaking to a joint session of Congress in 1866:
“I find no fault with the introductory clause, which is simply declaratory of what is written in the Constitution, that every human being born with the jurisdiction of the United States of parents not owing allegiance to any foreign sovereignty is, in the languageof your Constitution itself, a natural-born citizen ...”
There are analysis by Joseph Story, by Alexander Hamilton, and a dozen other constitution scholars affirming this definition. The efforts to obfuscate this well understood concept, which predates Vattel’s Law of Nations by millenia, but which document John Marshall cites in his decision in The Venus will continue until the courts resolve Obama's eligibility, or until we lose our 1st amendment as well as Article II.
As our republic is being dismantled it will be essential for those of us who resist to understand that the public face chosen for this revolution is not eligible to be president. My suspicion is that those who chose Obama - the Shadow Government - have never had much regard for the constitution, and most have only read it with distain if at all. Quite a few in legal academia have written devious articles to provide cover for some of the misleading nonesense about the definition of natural-born, and to provide cover for McCain, who is not a natural-born citizen. (That is why McCain was supported by the state-run media; his presence on the ticket silenced republicans.)
I don’t dismiss the possibility that McCain, who has received significant support from Soros over the years may be a willing participant. Some evidence for that is the promotion by the Republican party of Bobby Jindal, neither of whose parents were citizens when Bobby was born, as a presidential candidate. I definitely prefer Jindal’s political views to Obama’s, but believe that protecting the Constitution is critical to the survival of our republic. If our courts don’t address Obama’s ineligibility, and you can be sure all the justices know who John Marshall is and understand the definition of natural-born citizen, precedence will establish that the citizenship of parents is no longer necessary, and the child of illegal alien terrorists, born on our soil, would be eligible to be president. Illegal aliens may well elect our next president anyway, and probably had no small role in electing this one.
No one in our legislature dared to ask about Obama’s eligibity as they were required by oath to do - to defend and protect the constitution, and Article II Section 1 is part of our constitution. The 10th Amendment is a memory and the 1st Amendment is about to follow.
Had only those in the media, including supposed conservatives, understood that if they did keep quiet, threatend or not, they would still lose their radio stations, income, and future - Mark Levin, Hannity, and even Rush, (since a few jokes about birth certificates is not the issue). The silly schoolyard name calling is sadly effective, and reflects the state of reasoned dialog, of education, on both sides. The Obama supporters don’t have reason on their side, but cleverly use Alinsky tools to silence questions. That can only succeed because so few Birthers understand the real issue - that Obama's father's citizenship disqualifies his son from our presidency. It is a mess, but it is a fact. The longer the courts or military put off forcing our supreme court to clarify the issue the worse matters become.
In case you are honestly inquiring about the reasoning behind and meaning of natural-born citizen here is a reference to one of the most clear analysis, written by Joseph Story in 1833 on Article II Section 1. Story assumes you know the Vattel definition of natural-born, and cites Vattel as a principle source, but he elucidates the reasons for the natural-born requirement for presidents:
http://press-pubs.uchicago.edu/founders/print_documents/a2_1_5s2.html