We're using different definitions
By S&D "not working" you mean it is creating a negative situation for workers by driving down wages for Americans who want to do the jobs illegals are doing instead.
By "not working" I assumed you meant S&D wasn't doing what it does. In this case, driving down wages for Americans who want to do the jobs illegals are doing instead.
I never said S&D only creates positive suituations from the labor or any other perspective, just that it does what it does: Increasing the supply of anything (labor in this case) will reduce the price (wages in this case). Decrease supply and prices go up.
Where there is competition this is what happens.