Speaking to David Gregory over the weekend, Sen. Rand Paul took exception to the notion of a Republican "war on women" and called out Democrats as hypocrites for even talking about this given Bill Clinton's unethical relationship with Monica Lewinsky.
Bringing up Lewinsky (and in previous versions of this, San Diego Mayor Bob Filner) is a clear tell that the person talking doesn't even understand what the issue is. The "war on women" that is alleged to exist is a war of public policy. Specifically one in which conservative ideas are unfavorable to women.
Take, for example, the Affordable Care Act. Compared to men, women earn lower incomes and have higher average health care expenses. The Affordable Care Act taxes high-earning people (mostly men) and subsidizes low-earning people (mostly women) while also specifically restricting the ability of insurance companies to charge higher premiums to women. On retirement security, Republican policy is tilted in favor of tax benefits for people with investment income (mostly men) while Democrats love Social Security which is especially beneficial to unusually long-lived people (mostly women). Democrats want to make it easier for women to win lawsuits about gender pay discrimination while Republicans want to make it harder for them to do so. Democrats want to invest in the future by hiring lots of preschool teachers (mostly women, and a big help to people with child care responsibilities—i.e. also mostly women) while Republicans want to invest in the future with reduced marginal tax rates for high income individuals (mostly men).
Now of course Republicans object that these policies aren’t motivated by animus toward women. Republicans love rich female business executives like Meg Whitman and Carly Fiorina! Republican policies are very friendly to the interests of women who are happily married to prosperous men!
The flip side of this is that women tilt to the left politically in all rich democracies. This isn't about Todd Akin or something that's going to change by having Cathy McMorris Rodgers do more media appearance. A hefty chunk of politics is about the distribution of income, and until we have a country somewhere where women's market earnings and accumulated wealth are higher than men's, then that's going to push women to the left. As long as women are customarily charged with child care and elder care, then women's tendency to vote for the party that wants to publicly subsidize these things will be reinforced. And then you add in the whole suite of issues related to traditionalist religion and gender norms as the icing on the cake.