The analysis of this situation and, more importantly, the solutions urged are clouded by the fact that most people do not understand the gist of differential calculus.
What most people want is a society where upward mobility is unhampered, as it was in the 1800s, but where downward social mobility is almost completely restrained by the social safety net.
This is about like asking for a road that's very steep if you are going uphill, but very gradual if you are going downhill. People want that, too, but it's easier to make them see that it's impossible.
Liberty implies risk. The liberty to make choices that make you rich and happy implies the liberty to make other choices, one that will make you poor and miserable. Restrain one, and you restrain the other. It's that simple.
This is only part of the picture. Another part of the picture, one that I referred to last year, I think, is that the US is really two countries in one: a first world country with education, health care, and everything else equal to that of European nations, and a third world country surviving on little more than subsistence. And the immigration problem is just the tip of this iceberg.
However, keep your eye on Europe. Europe is rapidly becoming the same thing: two countries in one. The third world country inside Europe is muslim rather than Mexican, but it's the same phenomenon.