In fact, of four major polls conducted in recent weeks on the 20-week abortion ban, each one shows women are actually more supportive of the law than men.
A new Quinnipiac poll shows 60 percent of women prefer allowing unrestricted abortions for only the first 20 weeks of pregnancy rather than the Supreme Court-prescribed 24 weeks. Among men, 50 percent support the 20-week law — a 10-point gap.
A Washington Post-ABC News poll showed the gap at seven points, while two other polls (from NBC/Wall Street Journal and National Journal) showed it at six and four, respectively.
And those numbers may actually understate support among women for the new restrictions.
In the Post-ABC poll, rather than choosing between a 20-week ban and the current 24 weeks, 8 percent of women volunteered that abortion should never be legal, and 3 percent volunteered that the window should be smaller than 20 weeks. If you add them to the 60 percent of women who support the 20-week abortion ban, then 71 percent of women would seem to support the effort to increase abortion restrictions.
The Quinnipiac poll, meanwhile, shows 60 percent of women support the 20-week ban and 8 percent volunteer that it should never be legal, which again suggests that two-thirds of women could be supportive.
Support in the other two polls does not show quite as much support among women, but in each case, there are more women who support the ban than oppose it.
Taken as a whole, it's pretty clear that women are broadly supportive of the ban — and they support it in bigger numbers than men.
It's also clear that overall support for abortion rights is not a good proxy for opposition to abortion restrictions. People who think abortion should be legal, in many cases, are quite open to new restrictions.
Conventional wisdom on abortion has it that women are more supportive of abortion rights than men — and thus would logically be more opposed to restrictions — but polling shows that's not necessarily true either.
The Post-ABC poll showed 56 percent of men thought abortion should be legal in all or most cases, while 55 percent of women said the same. Over the past 20 years, there has been little difference between the two genders on this question.
The Quinnipiac poll does show that women support abortion rights more than men — 61 percent to 53 percent — but, again, it also shows women are significantly more supportive of the 20-week abortion ban, with just 25 percent opposed to it.
So what does it all mean?
It means that, if and when Republicans in the Senate push for a vote on the 20-week abortion ban (which already passed in the House), they can credibly make the case that they are doing something that women support.
Of course, that doesn't mean it will work, politically speaking. That's because, when it comes to the abortion battle, much of it is about intensity. And as Texas state Sen. Wendy Davis’s (D) filibuster shows us, pro-abortion rights groups and supporters — many of whom are women — will mobilize on this issue and press the idea that Republicans are anti-woman.
Republicans got plenty of heat in the 2012 election for their position on contraception and for rape-related comments made by some of their candidates. Those kinds of gaffes, which have repeatedly popped up whenever Republicans make an issue of abortion, can damage the GOP by reinforcing Democrats' argument that male politicians with extremist views are telling women what they can and can't do with their bodies.
But as of right now, there's little reason to believe that a 20-week abortion ban is the same kind of issue.
Indeed, it appears to be quite a politically viable move — both with men and women — and possibly even an advantageous one if Republicans play their cards right.
Scott Clement and Juliet Eilperin contributed to this post.