The suggestion that the American economy would stall and crash if the 10 million+ illegal alliens were to return to Mexico tomorrow, is garbage. Cheap manual labor tends to mask grossly inefficient practices in dire need of an overhaul. It's the easy way, the lazy way. But America didn't become great--it didn't set the standard for worker productivity--by taking the lazy route. I can think of nothing that would better jolt our prodictivity and make us even stronger than to eliminate the underground cheap labor market. Industries reliant on cheap manual labor would be forced to innovate and cut fat. Marginal companies would go under; their assets would be bought by more competent survivors. There would likely be well-paid spin-off jobs generated for US citizens who would effectively be outproducing cheap laborors 10 or 20 to one or more. Robotics (as you alluded to) is just one example.
Now, Mexico's economy might well collapse--and that's likely what's driving this. The present setup is perfect for Fox. He doesn't have to implement any substantial changes in the corrupt and woefully inefficient Mexican infrastructure. He pushes 10 million laborers across the border where American citizens in general (not the employers in particular) pick up the social and external costs (medical care, schooling, criminal prosecution and incarceration). In return untold billions of US dollars flow back into Mexico. Mexico bears no costs and picks up a windfall in greenbacks.