We are a commune of inquiring, skeptical, politically centrist, capitalist, anglophile, traditionalist New England Yankee humans, humanoids, and animals with many interests beyond and above politics. Each of us has had a high-school education (or GED), but all had ADD so didn't pay attention very well, especially the dogs. Each one of us does "try my best to be just like I am," and none of us enjoys working for others, including for Maggie, from whom we receive neither a nickel nor a dime. Freedom from nags, cranks, government, do-gooders, control-freaks and idiots is all that we ask for.
No, it isn't an idea, but as G. K. Chesterton put it, it is "a nation with the soul of a church." Before, nations were based on supposed common descent, or on conquest of one kin-group over others. America requires an ideology - however schismatized it may get.
We the People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defense, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, (emphasis mine)
"That any alien, being a free white person, may be admitted to become a citizen of the United States, or any of them, on the following conditions, and not otherwise:
...the right of citizenship shall not descend to persons whose father have never been resident in the United States"
Reliance of your argument on antediluvian naturalization laws, all of which were repealed by 1802, can be dismissed as impertinent. First, they do not define who is a citizen, but who among those foreign-born may become a citizen. Further, if the scope of citizenship had come to be more restrictive since, rather than less (as it has), there might be some merit in those exhibits – but alas…
As for the take on "posterity". It is not a synonym for "progeny", but means "the people who will live in the future after you are dead" [http://www.macmillandictionary.com/dictionary/american/posterity#posterity_3]
The idea that the imperfect Constitution, inspired by the more perfect Declaration, was founded "on common descent, with preference to one kin-group" is misconceived at best, but more like preposterous. If such were so, it certainly hasn't worked very well.
Geographically and cartographically, America is properly a continent. In common usage, "American" legalistically means one qualified to hold a US passport. But there's more to being American than the happy happenstance of residing in the land of purple mountains and amber waves of grain.
America is a transcendent nation of imperfect mortals bearing towards an ideal; a nation under God "dedicated to the proposition that all men are created equal" – as someone might have said.
How many of our solders would have ever gone for less?
Full-fledged Americans hold certain truths to be axiomatic, "self-evident" if you will. One can shun the philosophies of Locke and Jefferson and take up that of some other (such as Marx, Gramsci, Filmer, or some Hollywood celebrity), but regardless of passport, how is he yet distinctively, consummately American?