The preferred approach today would be to seek a federal grant to build the fence for “free”. Using govt contractors who would be paid Obama’s new minimum wage, of course.
The OP assumes that the low-skilled workers are as qualified as the higher-skilled workers at building fence line. Chances are however, the low skilled workers are going to have to build that fence 3 or 4 times before they get it right whereas the ‘’higher-skilled’’ worker is going to do the job right the first time, making him cheaper to use, even at a higher wage.