That's exactly what many people said about the Irish, the Italians, the Jews, and just about every group that came to this country in the 19th and early 20th century. In fact, one of the foundations of Planned Parenthood was Margaret Sanger's desire to halt these undesireables from reproducing (you can read it her works - she wasn't bashful about saying it!). Yet I think the Irish, et al., have turned out to be pretty good citizens, don't you?
One thing I do think we should do is bring back meaningful citizenship or Americanization classes. In the 19th and 20th centuries, children in public schools were taught in English, regardless of their parents' native language, and were taught about the history of this country, its political foundations and ideals, etc.
I think many immigrants, judging from my contact with Latin American immigrants in NYC, where they were suing to get their kids OUT of bilingual education, would be very happy to learn English and adopt American values. But with our crummy, left-wing, Dem-dominated educational system, their chances are not as good as they were in the 19th century, alas.
Do we remember that the idea of Germany for Germany was encountered on this issue just a few years ago? Is following Germany's lead what folks have in mind?
Also, it may be useful to keep in mind that this entire thing has been going on for decades. There are 20 year old anchor babies walking around. They were born to parents who are not US citizens. In fact, we could go back a generation and have a look at who fits in that category. Or wait, maybe more than one generation.
I suspect the more generations one goes back, the more people one will find who are not documented to have the proper genetics.