If they would ACTUALLY enforce the laws against illegal labor, the wages might go up, in a supply and demand fashion. Yes prices would fluctuate, but would most likely stabilize pretty quickly, but if "jobs Americans won't do" (one of my top three hated phrases) paid better, then wages across the board would go up, and actually have a foundation in SOMETHING besides federal fiat.
My plan:
1) Make hiring illegals economic suicide, something like a $1M fine per illegal that works for you. Fine doesn't apply if you participate in eVerify and keep the records for all employees(except in egregious cases like 50 john smiths with the same ssn), your illegal employees get deported.
2) Make welfare a bare bones safety net. You wanna live high on the hog, you gotta work. Same for food stamps. No increases for more children beyond a reasonable number, say 3.
3) Require proof of citizenship before you can qualify for even that level of welfare.
Make the environment hostile to those who would violate the law and there will be less incentive to do so.