I have discussed this before. I explicitly argued that this was one the GOP myths about taxes, and I lumped it together with the notion that poor people don't pay taxes (Myth #3: 50% don't pay taxes, including immigrants). Now a report from the Institute on Taxation and Economic Policy (ITEP) seems to confirm this view.
The report claims that undocumented immigrants living in the United States collectively pay an estimated $11.6 billion dollars each year in state and local taxes. And if their situation was regularized, they would pay even more. Add that to the fact that it does not seem that immigrants reduce wages, and the whole anti-immigration position seems more like what it really is. Xenophobia exploited by a demagogues preying on people that have had a hard time and are willing to find someone to blame. A dangerous mix.