I think this is part of the trend to get away from the pro-choice/pro-life dichotomy, as it the case with Planned Parenthood.
While it's all well and good to claim that most Americans support legal abortion, what it says is that supporting abortion in the public realm is becoming political kryptonite.
People support abortion the way they support legal strip clubs or legal porn sites. Maybe they want it legal because they may have recourse to it themselves once in a blue moon, it doesn't mean they really thing they're good in themselves.
The moral and cultural support for abortion is on the wane. Even if most people think abortion should be legal, that support is an inch deep.
When you just had a really crappy abortion experience, you don't want to talk to a radical abortion supporter because she's lobbying for the thing that is the source of your pain. You don't want to talk to a woman who may not have any moral qualms about the fact that you consciously chose to kill your unborn child, and you certainly don't want to hear how your own hypocrisy is politically instrumentalized by the likes of Joyce Arthur, who thinks of you as "anti-choice" because you have always spoken out against abortion.
Yes, of course they want to "get beyond politics" because that's the only way they see themselves "saving abortion" in spite of all the grief it brings.
Beautiful Pain? Hardly.