I think they should deport the illegals, but not to Mexico. Send them someplace worse. Maybe then they'd get the idea not to come any more. (Just send planeloads of them to the Sunni Triangle, Syria, Kazakhstan...).
Send them to Iraq or Afghanistan, then arrest them for being on the battlefield and send them to Club Gitmo.
Oh that is too harsh. I say deport them to the southern most tip of Brazil so it will take them a long time to get back here - say a week. ;^)