Can the GOP ever win the women vote?

[Mechaman]

White males and white females voted Obama in Rhode Island, Vermont and Massachusetts.

They did, but here was the breakdown.  White males (WM) in Rhode Island tied 48-48.  White females (WF) went 66-33 Obama, a 33 point gender difference.  

Vermont WM was 63-33 Obama, WF was 71-28 Obama, an 13 point difference.  Bigger than the national average, but not that big for New England.

Mass WM was 53-46 Obama and WF was 65-33, a 25 point difference.

The national average was about a point 9 gender difference.  Without New England, it would probably be 3-4 points.  Why is there such a big separation in the sexes in New England?  I am genuinely curious.  I made a map charting gender differences, but I don't yet have enough posts to display it.

I'm pulling this out of my ass, but I'm speculating that sex appeal has a little bit to do with how women in New England vote.  After all, a prominent tall and handsome Democratic candidate from the 1950's and 1960's liked tea parties.  And for good reason.

Not to mention, how many comparisons the media made between aforementioned Captain Sexy Abs and Barack Obama.

[Mechaman]

JFK won the male vote back in 1960, where Richard Nixon won the female vote, though the gap of both gender was extraordinary small.

Wow, that's pretty shocking.

[Mechaman]

Was the women vote for the Republicans back then due to being the party of women rights and the Dems being the backwards party?

Probably.
You have to remember that back in the late 1950's-early 1960's a lot of the Democratic party faithful were White Southern Males and Catholics.  Both groups that had quite the chauvinistic streak.  Meanwhile, the Republican Party at the time had been putting the Equal Rights Amendment (ERA) on the party platform since the 1940's (at least).
So yeah, something to that effect.