I've been using the wrong term - "native born". The proper term is "natural born", and "natural born" has been defined by Congress to include the children of citizens regardless of where they are born.
http://en.wikipedia.org/wiki/Natural-born_citizen US constitutional definition
The special term "Natural-Born Citizen" is used in particular as a requirement for eligibility to serve as President or Vice President of the United States. Section 1 of Article II of the Constitution contains the clause:
“ No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty five Years, and been fourteen Years a Resident within the United States. ”
Additionally, the 12th Amendment to the Constitution states that: "No person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States."
The Fourteenth Amendment to the United States Constitution provides an additional source of constitutional doctrine stating that birth "in the United States" and subjection to U.S. jurisdiction at the time of birth, entitles one to citizenship:
“ All persons born or naturalized in the United States and subject to the Jurisdiction thereof, are Citizens of the United States and of the State wherein they reside. . . ”
However, the full text of the fourteenth amendment does not mention the phrase "natural-born citizen," nor does it address Presidential qualifications. The phrase "natural born Citizen" is not defined anywhere in the Constitution.
Section 8 of Article I confers on Congress the power "to establish a uniform Rule of Naturalization..." This power has been construed to include defining the characteristics of a "natural born citizen", as well as the conditions of "naturalization".
The 1790 Congress, many of whose members had been members of the Constitutional Convention, provided in the Naturalization Act of 1790 that "And the children of citizens of the United States that may be born beyond the sea, or out of the limits of the United States, shall be considered as natural born citizens."