Good. I was hoping you would express it in this manner, rather than less than minimum wage (since, most illegal immigrants earn more than minimum wage, even day laborers).
So, if we get rid of illegal immigrants, regardless of whether or not we touch the minimum wage, the cost of labor increases. As such, prices increase, and these increases do not simply occur at the retail end, but also among producers trading with each other, as they require parts that they do not themselves produce. Thus, the prices increase throughout the market system. Moreover, the higher the wage, the more the company pays, per employee, in payroll taxes. So, again, prices increase.
Now, if prices only increase a bit, we are all worse off as citizens, though some citizens will have more job opportunities. However, as labor costs increase, moving the centers of production becomes more attractive to companies. That is, they will move away. They will still hire non-America citizens, they will just hire them in Mexico or elsewhere. And, we will pay the cost of the logistics required to deliver the products to market. Moreover, as labor costs increase, replacing human labor with machines becomes more and more attractive. Thus, we also get closer to the point in which we pay more to get our goods and there are less jobs.
You think all of this is worth it in order to simply make this one law sacred? Why wouldn't this also be worth it in order to give a few American citizens a living wage?