Bull$h!t! They are here for the freebies. Cut them off and most will leave. Put the credit card companies in charge of doling out the freebies, our gov't is too incompetent.
The best response to the ‘we can’t deport them all’ crowd came from Ted Nugent: “Mexico did.”
Better yet, cut off ALL unearned freebies to everyone. You paid into SS and Medi-scam, so they would continue. Make the indigent do something, anything, to EARN their keep. But documentation is required for that opportunity.
As you said, most will leave.