First, it would serve us well to define "nation." I agree with Mr. Renan in the sense that "Ethnographic considerations have... played no part in the formation of modern nations," and also that linguistic and religious considerations are equally inconsequential. I also agree with his argument that it is the wish of the people that creates a nation, though I disagree with the idea that a nation is "a soul, a spiritual principle." I posit that a nation is a social organization; and, like clubs, nations have entirely arcane prerequisites for membership.
What defines a nation is its exclusivity: in the case of the USA, the world is filled with people who want to be Americans, people that cherish and love the idea of individual freedoms and personal accomplishment (life, liberty, etc.). Likewise, France, for instance, is highly desirable for some, and Qatar is intensely desirable if you are a wannabe Olympian.
What does membership get you? Besides a home team and stuff like that, membership gives you access to all the primo perks of citizenship, such as a police force and a school system.
We adopt the notion of legitimacy practiced by the Concert of Europe, i.e. the notion that "if we say it's legit., then it's legit." Essentially, nationhood is a product of (1) the desire of the people to be a nation and (2) arcane and arbitrary exclusivity. You can't be a nation and let everyone in.
By this measure, the USA falls easily within the realm of nationhood.