When you figure a logical way to close the border as well as locating the illegals currently living in the unknown amount of unregistered rented rooms in this country. I'll accept your solution. But until then, I'll stick to my conclusion that we have to go after those who knowingly employ illegals
Let's put it this way, we can do a better job on the border than we're doing even if I were to grant you it probably can't be closed completely.
There are two effective ways of going after illegals: employer sanctions and assistance from the police. No not going door to door but only when they come into contact with them during their routine duties. The CLEAR Act pending in Congress will help with that as far as funding.
Once the law finally starts getting enforced illegals will stop coming and many will go home on their own as they did in the fifties.