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.
Illegals are cheaper with or without those considerations. All I see anyone doing is making excuses that don't hold water under scrutiny. The same is true with offshore labor. Even with removal of regulation, taxation and market based worker incentives gained via supply and demand - illegals and foreign nationals are cheaper by far than supply and demand generated wages within the US. Some want to point fingers at the minimum wage as though that were some big boogey man. It's bunk. Labor cost within a market is labor cost within the market. If you want to jump ship and then claim someone or something other than your greed made you do it - good luck. It's a prevarication Americans ain't buyin.