The idea that is America, is one of people bounde together by certain ideals, and not so much ethinicity, or even religion.
Best explained by three simple words found on the back of every dollar bill ever printed: "E Pluribus Unum".
There were no government documents printed in Italian and English. There were no separate Italian instructions when you called a toll free number or a government agency.
This was the message that I received as an immigrant in the early sixties: "Our culture (American) is dominant; your's (Italian ) is recessive; assimilate or be left behind.
My diet is still very much Italian (my first clue that American culture might be lacking was my introduction to the hotdog), I still speak Italian at home when I visit my parents. Even though I've only a high school education my English is spoken with near perfect diction, and without trace of accent. I gave up nothing throughout the process of assimilation and gained everything. It doesn't seem to me to be the same today.
That isn't to say I'm against immigation because I'm not. I realize that the reason so many hard working Mexicans come here is because it provides them with a better life. How can I possibly hold that against them? I also realize that I pay only $2.99/lb for mushrooms because the migrant worker will harvest them and my fat and lazy fellow Americans will not.
So God bless the immigrants of course, but I do think that the idea of America's greatness holds less sway than it did when I emigrated to the US.