Illegal Immigrants Work For Less

Eugene Volokh has an interesting post about the claim that illegal immigration is useful to our economy because immigrants are willing to do jobs that Americans won't do. Professor Volokh argues that in reality Americans won't do the jobs for the same wages that illegal immigrants are willing to work for, but if the illegal immigrants were not in the picture either the wages would increase and Americans would take the job or the jobs would cease to be economically feasible. So practically the claim should be:

"Illegal immigrants just do the jobs Americans won't do for the same low wages that illegal immigrants will take, and it helps our economy to have the jobs done at those low wages."

Here's something I don't get about the above claim. People who argue that illegal immigrants are necessary for our economy are implicitly recognizing the benefits of having people work for low wages, wages that are lower than the minimum wage. So what these advocates are arguing for is:

"We need illegal immigrants because they'll work for wages below minimum wage and that drives down prices, which is good for the economy."

Yet these same people strongly advocate a minimum wage for Americans. So it seems to be OK for poor Mexicans to work for low wages, in bad conditions, and receive no benefits, but claim that Walmart workers shouldn't receive full health care benefits, and they get all upset. Is that racism at work?