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Republican claims that the laws are not politically motivated and are solely intended to combat voter fraud were blunted somewhat when GOP state Rep. Mike Turzai, the House majority leader in Pennsylvania, was videotaped earlier this year saying that the state’s new law “is going to allow Mitt Romney to win the state of Pennsylvania.” (A spokesman said he was referring to the fact that Republicans would now be on a level playing field, and anyone looking further into it “has their own agenda.”) The new law requires voters to present government identification or a driver’s license to people before they can vote.

Mr. Bauer said regardless of whether the laws were passed in battleground states or not, there is a significant amount at stake — but that he thought turnout would end up reflecting popular will.

He added, though, that it would not come without a price.

“For a major presidential campaign to have to devote enormous time, effort and resources just to remove obstacles, basic obstacles to voting participation … strikes me as something to reflect on with some sadness,” he said. “I would rather not be spending as much time on this as I am.”