The problem with voter ID (and a whole lot of other issues like easyness of ID theft via SSNs) is that the US - as one of very few developed nations - has no requirement for a citizen to have a valid government issued ID card because of right-wing crazies.

The Left does not criticize voter ID per se, the Left criticizes that many people are effectively locked out from voting because obtaining ID cards can be an utter pain in the ass.