It is the guys the border patrol doesn’t catch that steal American jobs.
Well, no, that's completely false ... you've got cause and effect reversed.
There are no jobs to "steal."
The jobs belong to American employers, and some American employers quite often employ illegals rather than Americans.
The roots of the illegal immigration problem (and it is a problem) are to be found on the demand side; the border-crossers (the supply side) are simply taking advantage of the opportunities given to them by American employers.
If you really want to take care of illegal immigration, you might do better to address the demand/employer side of the equation; the illegal immigration problem will go away as soon as you take care of the demand side.