(I would post it as a comment to jace's original, but not everyone reads comments)
Up front, I agree with jace, but I also think we need to stop talking about immigration as if it were a problem at all. Precious few people in the United States have roots...truly native, First Nations roots...here in the first place. I may be a 3rd generation US citizen by birth, but 4 generations ago, my people weren't speaking Algonquian or Nahuatl. Freedom of migration should be accepted as a universal human right, as that would allow people to "pursue happiness" for real.
Really, the debate about immigration as a problem has more to do with racism than anything else.
In fact, thinking of the world as "nation-states" is gradually becoming archaic. Eventually it will be an outmoded way of sorting or claiming identity; it will have very little bearing on people's lives in the not-too-distant future. Look at Europe. In the EU, you may have a cultural identity, or "nationality", but in reality you are becoming more a citizen of Europe than your cultural homeland.
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