Employers who ignore safety rules and pay below minimum wage are as guilty as illegals are for being here. They should be prosecuted. If prices go up, so be it and the market will adjust itself. The market always adjusts itself.
Instead of giving away food stamps, housing allowances, AFDC, free phones, child credits etc. Give people these "jobs that no American will do" and allow them to earn some dignity and self respect at the same time. If you can keep the unions out if it, it will work just fine.
What we have right now is total dependency for millions of people. Slavery without the chains.
If you don't work, you don't eat. John Smith, Jamestown circa 1607. Seems like that policy worked out pretty well.