Sure, we're a "nation of immigrants," but at what point does one stop being an immigrant? How many generations does it take? And if I'm still an immigrant even though my family has been here for generations, then by rights I should have a "home" country that I can easily return to, but I don't. Sure, I could in theory immigrate back to Ireland and the UK where my ancestors came from, but you and I both know that no one would ever consider me "Irish" or "British." I would always still be an "American," which brings us back to the original question of how long it takes people to stop being immigrants.
You are what you are ethnically, that's it. No amount "living in America" will suddenly make you "American".
It's exactly the same for Russians for example, but in Russian we have 2 words to say "Russian", one of them implies ethnicity and the other one implies citizenship. You obviously can become "xxx citizen", but you never become the ethnicity, unless you already are.
Because I don't think we can speak of "US ethnicity", hence only "citizenship" remains. As such, anyone who becomes a citizen automatically looses "immigrant" status, even if only after a couple of years.