As to the first part of your post, that just shows how desperately those mothers want to have a better life for their kids, like Cuban Elian Gonzalez's mother who died to get him here only to have Castro get him back. If you think the Mexicans are coming to be permanent drags on the welfare rolls, there are two answers: First, even the Arkansas Antichrist signed off on sharp lifetime AFDC limits. Second, they have a lot higher ambition than welfare. What you are saying is what people said about Tommy Temper Tantrum Tancredo's Italian ancestors when they got off the boat 100 years ago. Tommy is now a real blueblood, I guess, and imagines he is descended from the Italian province that was located in Colorado or something.
Finally, the courts, wrongheadedly no doubt, have consistently ruled that you cannot deny public benefits to people on the basis of national origin even if they are not legally here. I don't like those rulings but they are what they are. Shall we abolish benefits or pay for them to be provided to the illegals, too? Those are the choices that the courts allow.
If the sore spot is jobs, let's get rid of NAFTA, GATT and WTO and there will be plenty of them for everyone. Remember that the AFL-CIO USED to be the bulwark against illegal immigration AND free trade because they did not like competition. I grew up on that in a union household. Now the AFL-CIO is largely gummint workers who fear no competition from illegals.
And that's why we're bringing in so much of the welfare-criminal class of Mexico and other countries. 43% of their children are born to unwed mothers ---- and that's only going to become higher, and our prisons are filled with grown children of this kind of family. We are destroying our country with these policies.