Abortion is the canary in the coal mine of personal freedom.

Yes.  That description fits quite well.  And I wholly agree that the privacy framing is a long-haul effort, although I do think it serves as a rallying point for the Left.

I still maintain that the greatest outcome the Dems could hope for, from a purely political standpoint, is the destruction of Roe.  (Setting that aside, this is a real-world, lives-at-stake kind of issue, and I'd rather keep it legal and fight the right-wing onslaught than go the End of Roe route.)  The Christian Right cares a great deal more about abortion than about issues like same-sex marriage, and they would have no reason to march for the GOP any longer, since, economically, they're much closer to the Democrats.  The "God Hates Fags" crowd makes up a much smaller percentage of the Christian Right, from what I've seen, than we sometimes fear -- not insignificant, of course, but not the real threat.

I whole-heartedly agree that the images of back-alley abortions and the like are the correct statregy, in the short-term.  The introduction from the NYT article says it all, as far as the privacy argument is concerned.  When a politician starts talking about the risk of government policing a woman's uterus, hospitals, and so on, I guarantee that people will react out of fear.  And, unlike the "threat from Saddam, it's not an irrational fear.

Be nice to America. Or we'll bring democracy to your country.