It's difficult to see how the Republicans are going to appeal to more women voters after killing the Violence Against Women Act (VAWA) at the conclusion of the 112th Congress. House Majority Leader Eric Cantor blocked the bill passed by the Senate; he simply could not abide added protections for American Indian, undocumented, lesbian and trans women:
Among the many items up for consideration at the conclusion of the 112th Congress was the Senate bill reauthorizing VAWA, which was originally passed in 1994. The Senate version had newly added tribal protections for American Indian women, granting tribes limited authority to prosecute sexual-assault crimes on their lands–whether the crimes are committed by American Indians or not. Cantor stood in the way of the Senate bill, offering instead the version the House passed, which excluded the new American Indian protections, along with those for undocumented immigrants as well as lesbian and trans women.
Though his actions indicated that he was against giving every woman in America the same legal protections against violent perpetrators, Cantor never articulated in public exactly why he was doing this.
...Why was Cantor so steadfast in his desire to block protections for American Indian, undocumented, lesbian, and trans women? All we do know is that while Republicans made compromises to avoid a so-called fiscal cliff, they were unwilling to do so in order to avoid dropping legal protections for women that have stood for nearly 20 years...