You're begging the question. His saying that means either:
1. He thinks this will suppress enough legitimate voters who would have voted Democrat to tip the scales (bad), or
2. He thinks there is enough widespread voter fraud on the Democratic side that eliminating the fraud will tip the scales, in which case it would actually be a good thing (unless you're coming down on the side of voter fraud).
BTW, I agree 100% with your overall position - establish voter ID laws, but don't do it in a disingenuous, last-minute fashion. That approach practically writes its own objections.