A more accurate statement would be...
"Jobs with wages too low for most Americans to take."
The status quo allows employers to pay lower wages than most Americans are willing to accept. In the not too distant past, these jobs were mostly menial ones like stoop labor, gardening, etc. Today, it has spread to much of the construction industry and some other non-menial jobs. Part of the problem seems to be that not enough Americans are entering the construction trades to meet the demand, but if wages get depressed because of illegal labor, then even fewer Americans will be willing to take these jobs. It becomes a self-fulfilling prophecy. These jobs can't be outsourced overseas but in essence the labor can be.