The problem with that is the tendency to look south, at the people coming across, rather than at the Americans who are paying them to come here.
Seriously: illegals come here for the jobs, or the welfare, or both.
Deal with the demand side, both among employers and government agencies, and the illegal immigration problem will pretty much end itself for economic reasons.
Actually you know what? Make an enterprise zone on the border. Part in Mexico,part here. If a business absolutely must have that sort of labor then they can build there. If there are too many that need jobs for that zone then screw them. They need to head back home one way or another. Of course extend no free stuff to those workers. The employers need to provide medical,no more running to hospitals on my dime. Build schools in that area too. Again,the business pay for them,not American tax dollars. I respectfully submit if you’re a business and that’s too much for you then you need to find another business not relying on illegal immigrants.