Tennessee had 154 blocked ballots in its March primary.

Keesha Gaskins, a senior counsel at the Brennan Center who has opposed voter ID laws, said she believes the numbers are significant and also underestimate the impact of voter ID laws. She said those numbers don't take into account people who were discouraged from showing up to vote in the first place or who may be turned away by poll workers. Even voters in states with less-strict ID laws may not get the proper explanation about how the process works without ID.

Beyond that, Gaskin said, rejecting even hundreds of ballots in an election is significant.

"These are still people who attempted to vote and who were unable to do so," Gaskins said. "When you compare that to the actual evidence of fraud, the difference is exponential."