The probable origin of the "Obama sues to restrict military voting" charge that the Romney campaign is making:
On July 17th, the Obama for America Campaign, the Democratic National Committee, and the Ohio Democratic Party filed suit in OH to strike down part of that state's law governing voting by members of the military. Their suit said that part of the law is "arbitrary" with "no discernible rational basis."
Currently, Ohio allows the public to vote early in-person up until the Friday before the election. Members of the military are given three extra days to do so. ...
I think it's unconscionable that we as a nation wouldn't make it as easy as possible for members of the military to vote. They arguably have more right to vote than the rest of us ...
Once you accept that, then it's easy to dismiss suits that call for equal ballot access.