All you need is dynamic that anytime an illegal uses certain designated services they are running the risk of exposing their status. Let them deport themselves.
Welfare, social services, health care, wire transfers should have a a citizenship check or residency status check (passport / birth certificate / green card /visa ) during processing. It's not necessary (and perhaps not legal) to deny service, but illegals need to know that their status can be checked.
This tactic is in the same vein as census citizenship question that's driving the dems bonkers. Aliens are afraid to show their status and won't take part. Lower pop counts will re-arrange house seats.
Looks like the old military technique in adopting a new rule some schools used back in the day. Announce the shit out of it, then just hammer some poor bastards who don't want to abide by it on day 1. Couple of days is all you need for the desired effect.