House Republicans have backed off a bill aimed at halting abortions after 20 weeks of pregnancy, after a group led by two GOP women raised concerns that it was too restrictive when it came to rape victims.

As The Fix Boss argued here, that's probably the right call for the GOP, because even broaching the issue would feed the so-called "war on women" narrative that Democrats have made a centerpiece of their electoral strategy. And Republican leaders don't really want to keep waging the culture wars.

But while that point is well-taken, and abortion as a whole is clearly a very divisive issue, the 20-week ban is actually a little different. That's because one side is clearly more popular than the other. And it's the side the GOP is on.

A Washington Post-ABC News poll in July 2013 showed 56 percent of Americans wanted to shorten the window for abortions from 24 weeks to 20 weeks. Another 10 percent volunteered that they wanted a smaller window or no abortion access at all. So that's two-thirds who wanted to restrict the current 24-week window in some way, shape or form, compared to just 27 percent who wanted to keep it at 24 weeks.

Other polls around the time showed similar splits.

A Quinnipiac University poll showed 55 percent preferred the 20-week option, while 30 percent preferred the current 24 weeks. Another 7 percent volunteered that abortion should always be illegal. And a Huffington Post/YouGov poll showed a 59/30 split in favor of 20 weeks.

What's most interesting about these polls is that they actually showed higher support for the change among women than men. Both the WaPo-ABC poll and the Q poll showed 60 percent of women backed the change to 20 weeks.

And yet here we are. The GOP, despite having all that apparent public support, is backing off its push.

But it's not really that surprising. After all, the polls asked a pretty broad question, and in legislating, the devil is often in the details.

Which is what happened here. You see, there was one poll that showed considerably lower support for the 20-week ban. It was from the National Journal, and it showed 48 percent in support and 44 percent in opposition.

For a clue as to why support was lower, just look at how the question was asked (emphasis ours):

As you may know, the House of Representatives recently approved legislation that would ban virtually all abortions nationwide after 20 weeks of pregnancy, except in cases of rape and incest that are reported to authorities. (Supporters say the legislation is necessary because they believe a fetus can feel pain at that point of the pregnancy.) (Opponents say it undermines the right to abortion that the U.S. Supreme Court established in 1973.) Would you support or oppose such legislation? 

That same exception in bold above is the one spotlighted by Reps. Renee Ellmers (R-N.C.) and Jackie Walorski (R-Ind.) as too restrictive. It wasn't included in the other polls mentioned above.

It's impossible to say whether that clause was definitely the reason for the lower level of support in the NJ poll. But if nothing else, it's a telling little nugget about what happened in the House Republican conference on Thursday. The GOP took something that was popular, but it got caught up in the details and politics of the day.

Update 4:04 p.m. Saturday: Turns out a later Quinnipiac poll did, in fact, mention the reporting requirement, using almost the exact same language as the NJ poll. By contrast, this poll showed support still at 60 percent, with 33 percent opposed. So that doesn't really explain the gap between the polls.

Here's the full question:

As you may know, in 2013 the House of Representatives approved legislation that would ban virtually all abortions nationwide after 20 weeks of pregnancy, except in cases of rape and incest that are reported to authorities. Would you support or oppose such legislation?