You don't have to. You simply publicize the 20 raids per week to be made at the outset. Raid large, medium, and small businesses. Make examples of them with big fines and jailtime as called for in the existing U.S. Code. Execute the existing law and the existing penalties for employing illegals.
Once business owners see that this is serious business, they'll stop employing them.
And without work, the illegals will go home.
By the way, if a business cannot survive without the use of illegal labor, that business shouldn't be in business.
I would also add to that some publicized raids on private, well-to-do homes, fines on citizens who have illegal nannies and gardeners. Make them all scared of La Migra again, and they WILL deport themselves.