The Obama administration scored another voting rights win on Friday when the U.S. Court of Appeals for the 6th Circuit said the key swing state of Ohio can’t single out military voters for special treatment – a ruling that will re-open a three-day weekend voting period that’s become known to black voters as the “souls to the polls” program.

Most Electoral College analysis lists Ohio as the most critical swing state for Mitt Romney. The Rasmussen Reports poll had Romney trailing Obama by 1 point in Ohio after Wednesday night's debate. It’s widely believed that military voters are likely to favor Romney while other voters who take advantage of early voting at higher than average rates – minorities, the elderly and the poor – have stronger attachments to Democrats.

The Romney campaign this summer seized on the Obama administration’s decision to confront Ohio’s Republican Secretary of State, Jon Husted, about the decision to close weekend voting to all but military members as a slap against the military. (Husted said he did it at the behest of election officials who wanted the weekend before the election to prepare the polls.) But the campaign said it was about equal opportunity, and the federal circuit court largely agreed.

Obama vs. Romney 101: 5 ways they differ on jobs

“The public interest … favors permitting as many qualified voters to vote as possible,” wrote federal Circuit Judge Eric Clay. Judge Clay said it would be “worrisome” if states “were permitted to pick and choose among groups of similarly situated voters to dole out special voting privileges.”

The focus across the nation on integrity and access to polls highlights the massive stakes for both parties around new voter registration and turnout.

While Republicans in 18 states have since last year instituted a slew of voter ID and voter registration rules in an attempt to ensure a clean election, the courts continue to frown on those, in 11 cases so far ruling in favor of easy access over fraud fears. Voter ID laws have been struck down in South Carolina and Pennsylvania, and courts have ruled against strict voter registration rules Florida.

“In the presidential race, it’s hand-to-hand legal combat, with almost every battleground state embroiled in a struggle over voter eligibility,” writes media critic Jonathan Alter in an op-ed for Bloomberg News.

In Ohio, early voting, including on the weekends, has become very popular, especially among blacks. Over 13 percent of the entire black vote came during the early voting period in 2008, compared to 8 percent of white voters who voted early. In all, 93,000 Ohioans voted in the three days leading up to the 2008 Election Day.

But Republicans in Ohio, Georgia, Florida, Tennessee, and West Virginia have begun to roll back some of those early voting rules, including restricting Sunday voting, after the 2008 race.

"It just so happened that this was the first time that early voting had been used in large numbers to mobilize African American and Latino voters," Wendy Weiser, who directs the Democracy Program at the Brennan Center for Justice at New York University School of Law, tells the Huffington Post.

The key sticking point for Republicans has been accommodations for special groups of voters versus the right of states to ensure voting integrity. It’s not an extreme position. Two-thirds of Americans want tougher restrictions, such as voter ID, at the polls, even though many critics liken such restrictions to Jim Crow-era poll taxes.

When Florida passed a tough new voter registration law last year, a sponsor, Sen. Mike Bennett, said he didn’t “have a problem making [voting] harder. I want people in Florida to want to vote as bad as that person in Africa who walks 200 miles across the desert [to vote]. This should not be easy.”

That sentiment has been echoed by officials in Ohio.

“I guess I really actually feel we shouldn’t contort the voting process to accommodate the urban – read African-American – voter-turnout machine,” Doug Preisse, chairman of the county Republican Party and elections board member, wrote in an email to the Columbus Dispatch. “Let’s be fair and reasonable.”

To some, a Republican peel back of early voting is “a clear strike at ‘souls to the polls’ campaign that encourage African-American voters to go vote after church before Election Day,” writes Brentin Mock, a reporter for Colorlines.com.

Democrats have claimed victory in most of the court challenges, and their passion around voting rights, especially on the political left, is understandable. Voter registration analysis suggests that new voter sign-ups in key states like Ohio, Iowa, and Florida have all lagged dramatically behind the surge that came ahead of the 2008 election, when the US elected its first black president.

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That discrepancy, political experts say, can’t be completely chalked up to tougher registration restrictions imposed by Republicans. It also speaks to the Obama campaign’s difficulty in mustering the enthusiasm of 2008 amid high unemployment, falling median incomes, and a steadily rising federal debt.

Obama vs. Romney 101: 5 ways they differ on jobs