Mostly what happens in those cases is that ppl just don't vote. And that is, of course, the goal in making it more difficult to do so. The (R)s will discover by and by though that they are shooting themselves in the foot because it's not just (D) voters who will get shut out.
Let's pretend though that the goal is to keep illegals from voting. According to every Reichwinger around, illegals have easy access to welfare, food stamps, free medical care, and so on. All of those things require some form of ID when applying. So wouldn't the same illegal person's ID used to get free American bennies also suffice as an ID at the polling place?
When did our founders argue that everyone should vote. Hell, they rightly distrusted low information morons so much they created the electoral process to ensure the mental midgets weren't the last say.
Voting is a PRIVILEGE, not a right. It comes with responsibility. Like being an informed voter and not someone choosing dishonest professional politicians who promise them something for their votes.