The USA did once belong solely to whites - well, white males and particularly wealthy heterosexual white males - and they are in many ways losing it to women and other ethnicities and sex/gender identities. Gays are not going back in the closet, and despite the racist garbage rising to the surface right now, we did manage to elect a black man as president.
So let's celebrate the decline of that America, the one in which a black man could be lynched for looking at a white woman the wrong way, the America in which that same woman could be raped by a white man that very night and have no recourse at any level of our justice system.
And let's be honest about who built America and the conditions under which they labored: slaves, Chinese immigrants, Native Americans, women and other peoples of all races.
However, we need to be careful here. People are not able to lay claim to America because their ancestors were here on the Mayflower or fought in the civil war. They are not able to lay claim to this nation because people of their ethnic group have been here just as long as or longer than white Europeans. No, one of the great virtures of America - existing, as always, more in potential than fact - is that the immigrant fresh off the boat has as much claim to the American dream as those who can trace their family history on this continent back centuries. (Even and especially ridiculously good-looking British ex-pats living in Florida.)