I like the Ike method.
Cut-off all welfare and Threaten to place the iron boot on their necks, and the Americans who employ them and they will make a run for the border (sorry, Taco Bell) before a wall can even get started.
They will self-deport
Still have to build the wall.
Otherwise, when the heat is off a little, they will just come streaming back in.
The odor of cheese is irresistible to rodents.