North Carolina State University students wait in line to vote in the primaries at Pullen Community Center on March 15, in Raleigh. (Sara D. Davis/Getty Images )

Voter ID laws have swept across the United States in recent years, following big GOP gains in the 2010 and 2014 elections. With Republicans now more powerful in the states than they've been since the Great Depression, it has been a priority for them from coast to coast.

The stated purpose of these laws, of course, has always been that they prevent voter fraud; you need to have ID to verify your identity for other things, after all, so why not voting? And polls generally show a strong majority of Americans agree.

But as any voter ID opponent will tell you, there are so few cases of documented voter fraud that it's not clear there's actually an ill that's being cured. Instead, Democrats allege that these laws are clearly aimed at disenfranchising minority voters, in particular, because they are less likely to have the proper IDs. And minority voters, of course, heavily favor the Democratic Party.

Assisting Democrats in this argument that it's all a partisan power grab? A handful of unhelpful Republicans who have suggested in recent years that voter ID does indeed help the GOP — perhaps so much that it would put them over the top in blue-leaning swing states like Wisconsin and Pennsylvania.

Freshman Rep. Glenn Grothman (R-Wis.) became the latest to stumble into this territory this week, including voter ID as part of his case for why Republicans could win Wisconsin in the general election for the first time since 1984.

"I think Hillary Clinton is about the weakest candidate the Democrats have ever put up," Grothman said, before volunteering the following: "And now we have photo ID, and I think photo ID is going to make a little bit of a difference as well."

It wasn't the first time, though, that Grothman has suggested as much. Back in 2012, when he was a state senator, he also predicted voter ID could have helped Mitt Romney win his state. Asked if it could make the difference in a close race, Grothman agreed that it could.

"Yes, right," he said, according to clip posted by the liberal ThinkProgress. "I think we believe that, insofar as there are inappropriate things, people who vote inappropriately are more likely to vote Democrat."

Perhaps the most well-publicized example of this belongs to then-Pennsylvania state House Majority Leader Mike Turzai (R), who said even more clearly in a 2012 speech that voter ID would help Romney carry his state.

"Voter ID, which is going to allow Governor Romney to win the state of Pennsylvania: done," Turzai said while listing his legislature's accomplishments.

It didn't help when, after the 2012 election, Pennsylvania GOP Chairman Robert Gleason agreed with the statement that the attention drawn to voter ID probably helped Republicans. (Voter ID hadn't actually been implemented yet, but we'll get to that.)

"Yeah, I think a little bit," Gleason said. "We probably had a better election. Think about this: We cut Obama by 5 percent, which was big. A lot of people lost sight of that. He beat McCain by 10 percent; he only beat Romney by 5 percent. And I think that probably photo ID helped a bit in that."

And then there's that infamous 2013 "Daily Show" interview of a local North Carolina GOP precinct chairman who said he was okay with it if voter ID prevented "lazy blacks" from voting.

"The law is going to kick the Democrats in the butt," Don Yelton added. He was later asked to resign over his racist comments.

Each time a GOP official says something like this, Democrats get understandably excited. Aha! they say, here's proof that the laws are actually aimed at disenfranchising minority and/or Democratic voters and helping Republicans!

Apart from the last case, though, that's drawing an extra line or two between what these Republicans are saying about voter ID and its impacts. As noted above, Pennsylvania didn't even wind up having voter ID in the 2012 election, because it got hung up in court, and Gleason was merely talking about the debate over it helping Republicans. Given that polls show it's popular, there's a case to be made that's true.

When it comes to the other examples, a more charitable read is basically what Grothman said in 2012: Republicans believe voter ID combats voter fraud, and voter fraud is more likely to be perpetrated by Democrats.

That, of course, is highly debatable. And what's more, saying that voter ID would do enough to actually help Republicans win states they otherwise wouldn't would require it to stop a significant amount of voter fraud — which, again, has never been documented.

All of which is to say that Grothman and other Republicans can probably defend their comments accordingly. But they're doing so on awfully shaky ground. And any time you hail the passage of a law as potentially helping your side win elections, you're basically begging to be accused of passing it for the wrong reasons. Which is a really unhelpful thing for Republicans.