Does the quality of the immigrant matter?
I think it does.
Now, they may or may not want to work, but they definitely want to be "paid" by any means, primarily government handouts, and the concept of being an "American" isn't even on the list. They want to be Mexican, Somali, or whatever else, and be eligible for the largesse that "America" will provide, but they want to make it change to accommodate them.
And that is the best case scenario. This is the likely one: