Ramsays arguments were rejected by the first Congress. The opposition debate was lead by James Madison, who said in response to Ramsay, “It is an established maxim, that birth is a criterion of allegiance. Birth, however, derives its force sometimes from place, and sometimes from parentage; but, in general place is the most certain criterion; it is what applies in the United States.”
http://memory.loc.gov/cgi-bin/ampage?collId=llsp&fileName=037/llsp037.db&recNum=15
Oops. That should pretty well settle that. Those who actually wrote the Constitution rejected the notion that citizen parents were required to be a natural born citizen.