Personally, I think heading into a voting booth is plenty of probable cause. People who aren't legally eligible to vote are having a significant impact on our freedom -- much more serious than being required to flash an ID card. Illegal aliens, felons, people voting multiple times under different names (often under the guidance of leftist unions), are voting themselves "rights" to OUR money. And they vote in politicians and judges who ensure that nobody is allowed to stop them from doing this. I'd a lot rather produce ID whenever asked, than have the government confiscating huge chunks of my hard-earned money to provide schooling and medical care to illegal aliens, endless stints in "rehab" for drug and alcohol addicts, and all sorts of other expensive abominations.
We're not talking about voting booths here, and you don't get arrested for showing up at a voting site without ID.
Voter ID is used only to ensure you vote once in your appropriate jurisdiction.