I've heard the "we depend on illegal migrant workers to keep food affordable because they are the only people who will work for $3/h" line a few times and it usually comes from the 'anti-wall' folks.
Farmers and other ag/food processors can mass import immigrants on special visas for farm labor. It's usually seasonal but I would imagine with a wall it would have to change, especially if workers have US dependents.
Most illegal immigrants also simply over stay their legal visas.
I've always thought that was a terrible argument. The same logic could be used to justify slavery since our food price would drop even lower. Work conditions aren't much different for illegal laborers compared to slaves anyway. If they complain they get deported