My suggestion--which might get pulled--is this:
Every time the INS rounds up an illegal, he or she receives a tattoo on their rump. Seal of the INS or something.
"Amigo, we catch you here again with this tattoo, we line you up and shoot you."
Naturally this has to be serious--and followed through. Perhaps it needs legislation. Maybe even a Constitutional Amendment.
(But the Constitution is badly broken anyway; the Fourteenth Amendment needs to be repealed anyhow. We need to base citizenship on blood, not location. If either parent is a citizen, so is the child. If neither is a citizen, neither is the child.)
Please feel free to pass this idea (tattoos) up the line. I am completely serious.
--Boris