When I was a kid I used to hear my grandfather (on my father's side) make the same comments about how immigrants had been coming into this country for years taking jobs away from good, hard working Americans and ruining what people like he had worked so hard to build, only the 'minority' that he was haranguing about had been the Irish.
America has always been a country with a steady flow of incoming immigrants, many legal but often many others who were undocumented. For example, my mother's father, while on a weekend visit from Canada, decided to simply stay and never went back, although a few years later he was naturalized so I guess you could say that he was eventually 'documented'. And then there were the first members of my father's family who entered the country as mercenaries after running the Union blockade during the Civil War. You could hardly call that a legal entry.
As for minorities, as in the example of my grandfather's views, every group of immigrants, irrespective of their racial or ethnic backgrounds, have always been treated as 'minorities' deluting the 'purity' of our society at that particular moment in time.
And this hits close to home in our own family, not because of the irregularities of my ancestors 'immigration' status as they were all middle-European (Flemish on my mother's side and Alsatian on my father's) so one generation in, who could really tell one way or the other. No, I mean my current and future grandchildren. Our four granddaughters are technically Asian-American and the newest grandchild, expected in June, will be Hispanic-American. And who will say that we're not a typical American family or that our extended family does not represent what is the best of America today? No, WE ARE the America of today and if there are those who are uncomfortable with that, well it's THEIR problem not ours and it certainly isn't anything that will diminish America's greatness nor undermine it's 'exceptionalism'.