Grab an 18th century dictionary, for crying out loud.
I've been studying this issue since 2008 and i've learned a lot of interesting things about it since then. One of the most significant things I have learned is that the word "Citizen" was not in common usage in 1776, and it did not mean at the time what it has come to be known to mean nowadays.
In English usage of the 1770s, the word "Citizen" meant "resident of a city." It was an amalgamation of the word "City" and "zen" as in "denizen." It literally meant "Denizen of a City."
The usage of the word to describe a member of a Country was not an English usage of the word. Blackstone and Shakespeare both use the word exclusively in the context of being a member of a specific City.
Usage of the word to describe membership of a nation was pretty much unknown to the English speaking people's of that time period. This usage of the word only occurred in one place in the world at that time; Switzerland.
This is understandable because Switzerland was the only country in the world at the time which was created from a collection of "city-states", of which there were incidentally thirteen of them. :)
The Swiss founding document "Charte des prêtres, Pfaffenbrief." (1370) is probably the first known usage of the word "Citizen" (Citoyen) to indicate membership in a Nation rather than membership of a city.
The point here is that the Founders were not originally familiar with the word in the manner that we use it today. It was a change to them when they adopted the Swiss usage of the word rather than the English usage of the word at that time.
And why would they adopt the Swiss usage of a word to replace the far more familiar English term "Subject"? Why indeed did they replace the word "Subject" at all? People would have us believe that we adopted the English Law methodology for creating subjects and then applied it to the word "Citizen", but if that's true, why didn't we just keep the word "Subject"?
It is clear the founders wanted to break from the word "Subject" both in meaning and in usage to describe the newly created members of the Republic, and so they adopted this Swiss word to convey this new relationship between the State and the Individual.
My point is that the word "Citizen" itself demonstrates that we followed Vattel's "Natural Law" , and not English common law. Had we intended to follow English common law, we would have kept using the word "Subject."