Democrats are stepping up their criticism of the White House’s voter integrity commission, while trying to stave off panic about the commission’s requests for data — panic that has already led to thousands of voters asking to be removed from the rolls in key states.

“It’s Republican overreach,” said Democratic National Committee Chairman Tom Perez in an interview. “This voter commission exposes the Republicans very clearly for what they’re trying to do, which is simply to suppress the vote. You look at the people on this commission and they’ve been the long-term leaders of the campaign to do that. It’s not hard to figure out.”

The pushback, informed by years of state-by-state voting rights battles, has become part of the DNC’s “Resistance Summer” push that was designed to involve the party in base persuasion and organizing earlier than in previous cycles. The Presidential Advisory Commission on Election Integrity, created after President Trump’s unfounded speculation that “millions” of votes were cast illegally in 2016, has created both a threat to organize around, and a problem that could undo the party’s voter registration efforts.

In several states, the commission’s July 1 request for voter data has led to a surge of voters trying to dodge the request by deregistering. In North Carolina, hundreds of people contacted the state elections office to inquire about their personal information, some of them asking about how to pull themselves off the rolls. In Colorado, an estimated 3,000 people have either suspended their registrations or asked that their information be made confidential, for a $5 fee.

Democrats have taken a delicate approach to the self-purgations. Perez said he was coordinating with state parties to urge voters not to take themselves off the rolls; Jason Kander, the former Missouri secretary of state who now runs Let America Vote, has been running a small social media campaign to urge against it.

But Democrats have also worried that giving the voter drop-off too much attention could spur even more of it. Their response is focusing more on the originator of the data request, commission vice-chair Kris Kobach, who has been Kansas’s Republican secretary of state since 2011. In an interview last week with Breitbart, Kobach speculated that voters taking themselves off the rolls were doing so either because they were caught out, or because they wanted to pull a stunt.

“It could be, actually, people who are not qualified to vote, perhaps someone who is a felon and is disqualified that way,” said Kobach. “Or someone who is not a U.S. citizen saying, ‘I’m withdrawing my voter registration because I am not able to vote.’ It could be a political stunt — people who are trying to discredit the commission and withdrawing temporarily because they are politically active but planning to get back on the voter rolls before the election next November.”

Perez, who scoffed at the theory that all of the un-enrolling voters had been voting illegally, said that Kobach was making himself infamous, and easy for the party to define.

“Our main message is simple — this commission is trying to make it harder for you to vote,” Perez said. “The remedy for what Kobach is trying to do is get out there and register your friends to vote to throw out Trump and his commission.”

The commission’s first public meeting is scheduled July 19, with access limited to reporters, but a live stream to be published on the White House website.