I know you would pay some jobs a lot less, those you aren't offshoring. Those you are trying to use illegals to fill because you don't want to pay a market rate where someone can live off their earnings. That's what got government involved in the first place - for right or wrong. Ethical shortcomings of business are usually the cause of government intervention.
Illegals are cheaper partly because you don't have to pay health insurance, SS, withholding taxes... Take those expenses out of an American's wage, and the pay we give to illegals looks pretty good in comparison. And they are, once again, all legislated.