In June, a group of labor organizations and advocacy groups sued Ohio to block enforcement of this requirement, arguing it could disenfranchise thousands of voters.

Ohio officials have argued the law is justified by the state's interest in "running elections fairly and efficiently."

"The argument is sometimes made that if states are required to count these ballots, more people would deliberately go and vote in the wrong precinct," said Wendy R. Weiser, director of the Democracy Program at the Brennan Center for Justice.

During oral arguments before a federal judge earlier this year, a lawyer for Ohio hinted at such a scenario when he challenged the strength of the plaintiffs' evidence. "Something else is going on that may not be poll-worker error," he said, as noted in a footnote to the judge's ruling.

In August, a federal judge ruled against Ohio's approach. The state's interest in fair and efficient elections, wrote U.S. District Judge Algenon Marbley for the Southern District of Ohio, "falls short of what is required to justify its inevitable disenfranchisement of thousands of qualified voters in the November 2012 election."

Ohio has appealed the decision, arguing that the rule helps with "counting only valid, legal ballots, in running a smooth election, and in minimizing post-election litigation." Allowing such provisional ballots to count, the state further argued, would make it "more difficult for elections officials to monitor and keep up with the voting process."

The Sixth Circuit Court of Appeals heard arguments in the case early last week and is expected to issue a decision soon.

Ohio tried to shorten its early voting period — until a federal court ruled otherwise.

Ohio used to permit in-person early voting for registered voters in the three days prior to Election Day. (More than 30 other states have similar early voting options, mostly for those who can't make it on Election Day.) But last year, the Ohio General Assembly limited the window. Early voting, which began Oct. 2, was scheduled to end 6 p.m. the Friday before Election Day. (Members of the military and overseas voters were exempt from the narrowed time frame.)

Democrats have been proponents of early voting: An estimated 93,000 Ohioans voted early in 2008. A subsequent University of Akron study concluded that early voters were "more likely to be strong Democrats than election-day voters" — including women, older voters and lower-income individuals.

In defending the law, Ohio elections officials argued that administering early voting the weekend before Election Day for all registered voters would interfere with counties' Election Day preparation, and that military voters have a unique need for being exempt.

In July, Obama for America, the Democratic National Committee and the Ohio Democratic Party asked a federal court to block the new rule, arguing that "tens of thousands of citizens who would have otherwise exercised their right to vote during this time period, including Plaintiffs' members and supporters, may not be able to participate in future elections at all."