You may be correct. I’d be satisfied with deporting criminals and potential terrorists. As to the others, perhaps issue them temporary renewal work permits. No government benefits at all and no path to citizenship, that can be revisited in 5-10 years. And a requirement they have/purchase health and auto liability insurance. No, not fair to American low wage earners, but perhaps doable with a Republican House and Senate.
No government benefits at all and no path to citizenship
Those two things would initiate self deportation at historic levels. Entice them with a ride home and few bucks. Some legitimate and effective enforcement in the workplace, they’ll leave.
And those that don’t will get restless and violent. Thus making it easier to forcibly send them home.