The last great wave of immigrants were met by those who understood that in order for them to partake of the great blessings of this country they must learn to live as Americans, and not as displaced whoever-they-were-before-they-came-here's. To that end the Settelment House movement proved it was one of the fastest ways for the newly arrived to acculturate and assimilate. (Yes, there were also some great injustices perpetuated by the Settlement House movement, but let's move past that for now.)
Nowadays, immigrants get off the plane or dry their feet and start looking for neighborhoods and communities filled with others just like themselves. There is no incentive to acculturate and assimilate.
I don't think that's absolutely true.
I think America's ability to absorb the great immigrant waves of the late 1800's and early 1900's was simply because that from Italy, to Poland, to Ireland... They were all still part of "Western Civilization" and all came from a background of a basic European Judeo-Christian backgrond.
And in large part, the massive influx of these people did indeed settle and look for neighborhoods of others just like themselves. Or economics and social stratification forced most of them there. New York, Chicago, even my own native Milwaukee had very well defined Irish, Italian, Polish etc neighborhoods. And to the outside "native" Americans from earlier waves, or with roots going back to colonial times those communities seemed as foreign as a Liberian or Somali one would seem today. And to a degree, those communities were often quite insular.
At the time other Americans viewed these communities with just as much suspicion and alarm. Protestant nativist Americans from English and Germanic backgrounds were very concerned about Catholics from Ireland and Italy who had "Fealty to the Pope and Rome". An attitude that lasted even up to the 1960's and was an issue in the election of John F. Kennedy as President.
I see parallels with that and Muslim immigrants today.
OTOH, there never was a "Catholic Court" movement that I'm aware of, unlike Europe and the United Kingdom, where there are efforts to set up Sharia Law and Banking, and there are now the first rumblings of that here in the Sates too... :|
I think the issue is: Within a generation or two, will non-European, non-Western Civ, non Judeo-Christian immigrant communities integrate as wholly as the 1880-1920 European waves did? Or are deep cultural barriers that will prevent it?