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The 2009 Military and Overseas Voter Empowerment Act ordered the military to set up a special voting-assistance office at every U.S. base around the world, to make sure troops can negotiate the patchwork of state registration and absentee voting requirements, and get their ballots mailed in time.

Last month, the Pentagon inspector general released a report saying investigators had been unable to contact voting assistance offices at more than half of the U.S. military’s 229 bases around the globe. Officials said they were using outdated contact information.

Defense Secretary Leon E. Panetta “believes, along with the rest of the department’s leaders, that it is vitally important for our service members and their families who have made great sacrifices in defense of this democracy to have their voice heard in this election,” Mr. Little said this week.

Some supporters of Republican presidential nominee Mitt Romney have accused the Obama administration of trying to stymie military voting, which usually is assessed to be more conservative than the general population.

Mr. Eversole dismissed that suggestion.

“I don’t buy that,” he said. “This issue long predates the current administration,” and has been characteristic of the Pentagon under control of both parties.

Mr. Eversole noted that the turnout among military voters in 2008 was 30 percent, less than half of the turnout in the population as a whole, but he declined to speculate about whether that number would be lower this year.

“I’m working every day to prove myself wrong, getting these guys to register and vote,” he said. “My hope is that we can right the ship, but we’re running out of time.”