The Republicans who devised the laws call them fair and necessary. In federal court, lawyers for Wisconsin have called its election rules “voter friendly” compared with those of many states, and said the court’s voter ID order was so lax that any excuse for lacking proper identification documents, including that “the DMV is haunted,” was sufficient.

But the crux of the Republicans’ argument is less whimsical: Tough election laws, they argue, are needed to keep Democrats from stealing elections. “What I find is that leaders of the other party are against efforts to crack down on voter fraud,” Gov. Greg Abbott of Texas, a Republican, said in March. Numerous studies and surveys of voting show the opposite: Election fraud is rare, and the in-person fraud that the laws could prevent is virtually absent.

Wisconsin, too, has been hauled into court for failing to obey a judge’s order. On Oct. 7, after Judge James D. Peterson of Federal District Court read articles in The Nation and The Milwaukee Journal-Sentinel documenting problems with the ID program, he summoned state officials to explain themselves.

The officials acknowledged flaws in the ID-issuing process and promised to fix them. But barely two weeks earlier, they had maintained in a report to the court that the ID process was running smoothly and that clerks in motor vehicle offices had been trained to deal with applicants.

That claim was belied when Molly McGrath, the national coordinator for the voting rights group VoteRiders, dispatched her mother to request help in getting an ID at 10 motor vehicle offices across the state. Few could navigate the application process. “They’re changing things so quick that it’s hard for us to keep up,” one clerk told her. Another, apparently unaware of the court’s order to issue IDs promptly, told her that “nothing’s guaranteed.”

Barbara Koester, 89, found herself unable even to register to vote after being erroneously told she first needed an ID, which required a certified birth certificate (it does not). “She was born in St. Louis, so I guess I could apply for a copy,” her daughter Ann Travers, who escorted her to the office, said in an interview. “But I don’t know how long that would take.”