The political dynamic is different in the US than Canada, obviously, but I think it's safe to use our most recent election as a model for what increasingly desperate Democrats will do in angling for the women's vote.
Paul Martin successfully used vague scare tactics intimating Conservatives would "take away a woman's right to choose." Never mind that such a policy wasn't part of the Tory platform, or that it'd never
pass even a free vote in the House - it'd have been political suicide (despite the fact that a large number of party members might have reservations about abortion-on-demand); the fearmongering won.
I don't know that there's a lesson to be applied, here. Scare tactics kneecapped the Conservatives despite proactively countering the baseless accusations, because Canadians were willing to believe the worst. However, the American electorate is much more evenly divided, with healthier (despite being dirtier) political discourse; both sides can slime each other, but at least there isn't the danger of one or the other being given exactly complete or exactly no credibility.