I'll ask again: These illegal immigrants are apparently earning an income and paying taxes (or they wouldn't be eligible for a tax credit). So apparently companies are hiring illegal immigrants (because they're cheaper) and then footing society with the bill of cleaning up the mess. Yet somehow only the immigrants are responsible?
If you factor in the EITC, they aren't paying taxes. They are receiving a net gain from the system in the scenario we are discussing.
Food stamps, cash welfare and free health care are also tax free.