In a report issued on Wednesday, the Brennan Center for Justice at New York University School of Law said it had found that obtaining proper voter identification in the affected states was difficult. More than 10 million eligible voters live more than 10 miles from their nearest ID-issuing office, and many of the offices maintain limited hours, the report said. Moreover, it said, despite pledges to make voter identification free, birth and marriage certificates, often needed for the process, cost $8 to $25, and many affected voters are poor.

The argument by the Pennsylvania law’s proponents that it has nothing to do with partisan politics took a blow late last month when Mike Turzai, the majority leader of the state’s House of Representatives, addressed a group of fellow state Republicans. Listing the accomplishments of the Republican-controlled legislature, he said, “Voter ID — which is going to allow Governor Romney to win the state of Pennsylvania — done.”

In Wisconsin, a voter identification requirement has been declared to be in violation of the state Constitution, but that ruling is expected to be appealed. Some Southern states, like Texas and South Carolina, have to clear any voting law changes with the Department of Justice under the Voting Rights Act of 1965. The department has rejected their identification requirements as discriminatory, and this past week Texas has been challenging that ruling in federal court in Washington. In September, South Carolina will take its case against the department to court.

One of the most closely watched cases is here in Pennsylvania, where polls show a tight race shaping up between Mr. Obama and Mitt Romney, the former Massachusetts governor.

“We don’t know whether voter fraud is a huge or a small problem, but we believe the new law will preserve the integrity of every vote,” said Ronald G. Ruman, spokesman for the Pennsylvania Department of State. “The goal is to make sure that every vote cast counts.”