On a related note, this is why there's a rather huge debate over whether or not someone should be required to provide identification when they vote.
Without trying to spark a partisan discussion, those taking positions against voter ID requirements are the ones you'd expect to be opposed to illegal immigrants voting, and those in favor of voter ID requirements are the ones you'd expect to benefit the most from illegal immigrants voting.
Meanwhile, both sides have framed the argument in ways that bring up everything except immigration.
In short, while I won't comment on who's right and who's wrong, the immigration debate in our country has nothing to do with immigration, and everything to do with the political windfall of which party gets to inherit the new voting bloc.