Absolutely, it's an option. And those that say it just can't be done are lying.
Checking citizenship against a database -- not a piece of paper -- at every encounter with police, school, medical care, employment, etc. and then bussing to the border anybody not in the database with a legal right to be here. No hearings, no extensions, just immediate transport out of the country.
How will these people be able to live here if they are denied all public services -- including school -- and employment ? They will self-deport or become criminals. If they become criminals, they will eventually be caught and deported.
As far as actively searching for them and deporting them, I'll bet a $1,000 bonus available to sworn peace officers would search out millions of them and cost us a relative pittance -- a few billion dollars spent on rounding them up would pay for itself in reduced cost of public services.
Yeah, actually many places PROHIBIT the police from asking immigration status.