If the government was serious about rounding them up and giving them the choice of being put to work in labor camps building a nice strong wall along the border or being dropped on the beach on the Ycatan peninsula by an amphibious ship, you can bet that there would be a stampede toward the border requiring no law enforcement at all.
The first step is to start prosecuting big employers of illegals to loosen them up and get them to break out into the open.
Start with Tyson foods.
LOL! I really like the way you think. Very creative.