The phrase, "Natural Born Citizen" comes directly from Vattel's treatise, 'Law of Nations', which learned men of the day (especially the Framers) were very familiar with.
I've done quite a bit of searching on that phrase since Obama was elected, but have found no colloquial references for it. It was essentially a legal term that defined a precise condition of citizenship (as defined by Vattel).
As far as I know, it may have been coined by Vattel himself.
I'm almost sure that I ran across another reference to NBC by one of the Framers in my travels, but all of my saved research is on the hard drive of a computer that's now FUBAR. I don't recall offhand now where I read it, or who it was that mentioned it.
Sorry to hear about your computer going screwey. I hate losing info like that. I’m aware of Vattel and it is very obvious that they got this general idea from Vattel. However, I find it interesting that the founders never really debated this term (that I know of) which was a vague and archaic term even at that time. Yet they put it in the constitution to say that the President had to meet a special qualification of citizenship. The very first Congress (of which many of the founders were in) went on to further refine this term to include U.S. citizens having babies abroad. That tells me that we know the general idea of the natural born citizen to be someone born here of American parents and it is up to Congress to qualify and refine this term further.
This same question of natural born came up when Goldwater ran. He was born in Arizona when it was a territory. Did that constitute “natural born”? There were also questions about Chester Arthur during his Presidency. His father was a citizen of Ireland at the time of his birth and there was always a question of whether he was born in Vermont or Canada. It’s almost an exact parallel to the Obama case. The questions were raised back then but nothing was ever proven one way or the other.