No one is naive enough to think we'll get them all. Round up the ones we do find, the ones pulled over for traffic violations and such. Refuse education to their children. Clamp down on their employers. Make their lives hell.
If it breaks up families, too bad. If a thief is busted, do we not throw them in jail because it might "break up a family"?
Make it so the worst criminal illegal aliens deport themselves, before they get thrown in USA prison for 10 years. Then others will self deport.