[LibFreeUSA]

-"...that person could be deemed ineligible to run."

What Section/part/wording of the Constitution would you reference to make this a valid legal claim that the courts would affirm?

[SoldierDad]

I didn't find it written into the Constitution, as you well know. I found the following statement at http://www.federalistblog.us/2008/11/natural-born_citizen_defined/:

House Report No. 784, dated June 22, 1874, stated, “The United States have not recognized a ‘double allegiance.’ By our law a citizen is bound to be ‘true and faithful’ alone to our government.”

and,

Whatever might had been the correct understanding of “natural-born citizen” prior to 1866, the adoption of the Fourteenth Amendment certainly changes the view because for the first time we have a written national rule declaring who are citizens through birth or naturalization. Who may be born citizens is conditional upon being born “subject to the jurisdiction” of the United States – a condition not required under the common law. The legislative definition of “subject to the jurisdiction thereof” was defined as “Not owing allegiance to anybody else,” which is vastly different from local jurisdiction due to physical location alone.

There is more on this issue written on that site.