Razib notes that men tend to be, on average, more pro-choice than women are, despite all the talk about a putative "war on women" being waged by the patriarchy. He traces GSS responses on the issue over the life of the survey and finds that in most years men are more inclined to the idea that there should be no restrictions on abortion than women are.
Restricting the time frame from the turn of the century to the present for contemporary relevance, we find the same: 41.5% of men and 39.8% of women think "it should be possible for a woman to obtain a legal abortion if the woman wants it for any reason" (n = 9,236). It's a dichotomous question that presumes that even if the father of the prospective child objects, the woman should be able to make the ultimate decision without offering any justification for her choice. In other words, the question is set up in a way that gives an individual woman maximal authority over her reproductive choices. Even so, men are more supportive of the idea than women themselves are.
The sex differences are marginal, though. The more consequential point is that while the issue is often framed as one in which there are stark sex differences in opinion, that's a total fiction, and an intentionally mendacious one at that, with the objective being to turn the largest 'minority' (which, of course, is actually a numerical majority) in the direction of the Democratic coalition in its unifying opposition to the heterosexual white male 'majority' (which constitutes less than one-third of the US population and is declining by the day).
This war-on-women strategy was parlayed into the the 2012 and 2014 national elections, although without much success. As Steve Sailer has pointed out on multiple occasions, the gender gap pales in comparison to the much larger marriage gap. Knowing whether a voter is male or female provides much less predictive power over electoral behavior than knowing whether a voter is married or not, irrespective of sex.
This phenomenon applies to the abortion issue as well. While there is less than a 2% gender gap in contemporary opinions on abortion, the marriage gap is five times larger, with 38.0% of married adults assenting to the idea of unrestricted female choice compared to 46.1%--nearly half--of never married or divorced adults (n = 8,450).
GSS variables used: YEAR(2000-2012), ABANY, SEX, MARITAL(1)(3,5)