How about rewarding bounty hunters for the capture of these illegals? Bounty Hunters could handle the situation quickly. word would spread among the illegals. Those areas willing to do this would save more from money normally spent on their social service costs.
(And also cause a few problems along the way.)
Someone sent me a video of a guy in LA going to a place where day workers congregate. He tells them he needs help on his deck, then proceeds to drive them to the LA office of the INS. He did it as a joke, but I got to thinking, what if people really started doing that? I would be pretty tough for the INS to ignore it if citizens started showing up with pick up loads of illegals....