As states around the country enact or consider voter-ID laws, the battle formations are well-rehearsed.

Conservatives who back the laws say that there’s a danger of fraudulent votes, which pollute the democratic process at best and swing elections at worst. Liberals who oppose them counter that there’s next to no evidence of actual voting fraud; that voter-ID laws wouldn’t stop that fraud anyway; and that the laws are actually intended to depress voter-turnout among the populations that are least likely to hold state-issued photo ID—students, the poor, minorities, and the elderly who are most likely to vote Democratic—and improve conservative prospects in elections, despite demographic changes that favor liberal candidates.

The pro-voter-ID side has two big problems. First, they’ve been unable to produce proof of the widespread voter fraud they believe exists. Second, people who agree with them—and in some cases the proponents themselves—keep slipping up and saying the point is to help conservative candidates.

Last week, Jim DeMint, the president of the Heritage Foundation and former senator from South Carolina, spoke on St. Louis-area talk radio. Legislators in Missouri are trying to place a constitutional amendment on the ballot that would mandate that voters show voter ID. (I explained why they’re using that path last week.) Host Jamie Allman asked DeMint about Virginia Governor Terry McAuliffe’s move to re-enfranchise former felons.

“The left is trying to draw votes from illegals, from voter fraud, a lot of different things, so this kind of fits right in to trying to find another group that they can basically count on to vote their way,” DeMint said. “So it’s really a bigger issue, and that’s why the left fights voter ID or any kind of picture ID to know that it is actually a registered voter who’s voting. And so it’s something we’re working on all over the country, because in the states where they do have voter-ID laws you’ve seen, actually, elections begin to change towards more conservative candidates.”

It’s that last part that progressives have seized on—DeMint’s statement that  “in the states where they do have voter ID laws you’ve seen ... elections begin to change towards more conservative candidates.” It suggests that the motivation is just what voter-ID opponents have suggested all along.

The rest of DeMint’s comment, though, is equally interesting. It offers a litany of ways he thinks Democrats are trying to steal elections—and frames voter-ID laws as one tactic to fight back. But his examples don’t really hold up. It’s unclear what effect McAuliffe’s move might have in 2016, and Nate Cohn at The Upshot suggests it might be relatively modest. Incarceration rates are widely racially disparate, so that more ex-cons are African Americans, and African Americans tend to vote heavily Democratic. Over the years, the push for felon re-enfranchisement has come from both sides of the aisle—former Senator Rick Santorum backed it during his 2012 presidential run—but Democrats have been especially eager to implement the reform. Some conservatives have been warning for more than a decade that felon re-enfranchisement is a Democratic ploy to win votes, and while it’s hard to imagine there’s no partisan motive involved, that’s not a compelling argument for excluding people from the body politic. DeMint’s comment about “illegals” is probably a reference to the idea that Democrats want to offer citizenship to illegal citizens to win their votes; the fraud question is, again, barely a question.

DeMint isn’t the first person to say something like what he did. “Now we have photo ID, and I think photo ID is going to make a little bit of a difference as well,” U.S. Representative Glenn Grothman of Wisconsin said the evening of the state’s presidential primary. A former chief of staff for a Republican Wisconsin state senator told The New York Times in a story published Monday that he attended a meeting where GOP lawmakers “were literally giddy” over the suppression effects of the law. The staffer, Todd Allbaugh, says he resigned in disgust.

In summer of 2012, the Republican leader of the Pennsylvania state house said that voter ID “is gonna allow Governor Romney to win the state of Pennsylvania.” (A judge blocked the law, and Obama won the state.) Around the same time, Doug Preisse, the chair of the GOP in Franklin County, Ohio, told The Columbus Dispatch, “I guess I really actually feel we shouldn’t contort the voting process to accommodate the urban—read African-American—voter-turnout machine.”

In late 2012, former Florida GOP Chair Jim Greer told the Palm Beach Post that the motivation for shortening early voting—another common tactic in recent years—was to drive down black turnout. “The sad thing about that is yes, there is prejudice and racism in the party but the real prevailing thought is that they don’t think minorities will ever vote Republican,” he said. “It’s not really a broad-based racist issue. It’s simply that the Republican Party gave up a long time ago ever believing that anything they did would get minorities to vote for them.” (Florida Republican leaders are quick to point out that Greer pled guilty to theft and money laundering three years ago.)

In 2013, Don Yelton, a local GOP official in North Carolina said on The Daily Show that the Old North State’s strict voting law “hurts a bunch of lazy blacks who wants the government to give them everything.” He was compelled to resign.

DeMint’s comments are interesting because of his stature as a former leading rabblerouser in the Senate and as the leader of one of the most important conservative organizations. Many of the other people to voice similar ideas have been either eccentric characters (like Grothman), minor local officials (like Preisse), or both (like Yelton). Coming from DeMint, the comment seems more important and telling.

But the pro-voter-ID side has two big advantages, despite these slip-ups. One is that the courts have generally been on their side. In North Carolina, a coalition of groups sued to challenge the state’s strict voting law, which instituted a voter-ID requirement, shortened early voting, and eliminated same-day registration, among other changes. Yet a judge ruled last week that while there was a history of racial discrimination in the state, he rejected any claims that the state law was intended to hurt African American or other minority voters. “Having considered the entire record as a whole, this court is not persuaded that racial discrimination was a motivating factor of HB 589,” Judge Thomas Schroeder wrote. “Accordingly, Plaintiffs have failed to establish that the legislature acted with discriminatory intent.”

The second advantage is popular opinion. Polls show that majorities of Americans tend to think that voter-ID laws are a pretty good idea. It’s going to take a lot more than one apparent Kinsley gaffe from Jim DeMint to change that.