Topeka ? Secretary of State Kris Kobach’s allies Tuesday revived the conservative Republican’s proposal to require first-time voters to prove their U.S. citizenship starting next month, but a vote in the state House advancing his bill sent mixed signals about its chances for passage.

The House gave the measure first-round approval on a 67-53 vote, suggesting supporters have enough votes to pass the legislation on final action, scheduled for Wednesday. The bill would go next to the Senate, where an earlier version of Kobach’s proposal is stuck in committee.

Kansas already has a requirement that people registering to vote for the first time in the state provide a birth certificate or other proof of citizenship to elections officials, but the rule doesn’t take effect until Jan. 1, 2013. Kobach wants to move the effective date to June 15, in time for a normal wave of registrations before a presidential election.

Kobach contends the rule will prevent election fraud by ensuring that illegal immigrants and other non-citizens don’t register to vote. His office found 32 non-citizens registered last year; he believes that is a fraction of the actual total, though there are no firm figures.

Kansas has about 1.7 million registered voters, and fewer than 10 cases were reported over the past decade of non-citizens voting or attempting to vote. Critics suggest a proof-of-citizenship rule is unnecessary and will suppress voter turnout, particularly among poor, minority, elderly and college-student voters.

Kobach and his supporters hope the Senate will take an up-or-down vote on the latest version of his proposal, rather than routing it through committee. Kobach said he believes a majority of senators are willing now to do it after talking to him and his staff.

“The debate over whether to have proof-of-citizenship has been resolved,” Kobach told The Associated Press. “Now is the question, do we do it when it makes the most sense?”

But Tuesday’s House vote was less decisive in Kobach’s favor than the 81-43 vote in February on the earlier version of his proposal.

House Elections Committee Scott Schwab, a conservative Olathe Republican and Kobach ally, said some lawmakers are getting nervous about county elections officials being able to adjust to the change and the state being able to educate voters in just five weeks.

“We’re getting close to that June 15 deadline,” Schwab said. “That’s a legitimate argument.”

Kobach has said repeatedly that he has a $300,000 voter education campaign ready the moment the change takes effect, and he’s confident that it won’t create administrative problems.

But it’s not just potential administrative headaches that are a question for critics.

Rep. Ann Mah, a Topeka Democrat, a vocal critic of Kobach’s proposal, said the change is likely to invite a costly federal voting-rights lawsuit. She accused Kobach’s allies of pushing a new version of his proposal in hopes of forcing senators to vote on it — and creating a campaign issue against those opposing it.

“Putting this before them and forcing them to vote on it gives them one more chance to look like the heroes and the adults in the room,” Mah said.