That might not work. A lot of women want a man in charge. Even the feminist ones- because the govt is their father. Women don't want the govt to be a mother- that is their job..
In the end, "What Difference does it make?" will be the slogan of whoever runs for the Dems. It wouldn't surprise me if this wasn't just a ploy to get an implicit 3rd term. Even if they won, I bet anything Hillary doesn't move into the White House. Or if she did, the Obama's wouldn't leave the master suite.