"But not even the most hardened nativist would be able to round up 12 million people and deport 'em all. "
Strawman argument alert!!!!
How about just making nearly impossible for them to get a job by punishing employers who hire them so severely (ala penalties for poaching) that no one will risk it? Would they not "self-deport" so we don't have to round them up and deport them?