Voter ID laws are not vote suppression. Voter fraud is also not a problem, at least on a large scale.
Republicans trot out avocation of voter ID laws to fire up their base, which thinks that there is a lot of voter fraud being committed by Democrats.
While it fires up the Republican base, it also fires up the Democratic base, who believe (I don't really think they believe this, but they claim to) it is a Republican plot to suppress the minority vote, which overwhelmingly votes Democrat. The soft bigotry of low expectations - poor minorities don't have IDs or can't get to a place to obtain one, so a voter ID law is suppressing their right to vote.