Do women have supreme ownership of their bodies or not?

Christianity Today recently interviewed Barack Obama, focusing mainly on his faith but the second page of the three page interview starts with a question regarding abortion and Obama's votes against prolife legislation. Obama responded by saying,

Ultimately, women are in the best position to make a decision at the end of the day about these issues. With significant constraints. For example, I think we can legitimately say — the state can legitimately say — that we are prohibiting late-term abortions as long as there's an exception for the mother's health. Those provisions that I voted against typically didn't have those exceptions, which raises profound questions where you might have a mother at great risk. Those are issues that I don't think the government can unilaterally make a decision about. I think they need to be made in consultation with doctors, they have to be prayed upon, or people have to be consulting their conscience on it. I think we have to keep that decision-making with the person themselves.

Obama is well-aware that "health" with regards to abortion has been expansively defined by the Supreme Court to mean whatever a woman can think of and an abortionist will agree to.

But reading Obama's statement here and numerous posts by pro-choice bloggers this week, I'm continually left scratching my head at how they don't see how their opposition to (at least for those who do oppose) late-term abortions completely undercuts their reasoning (women should be allowed to make these decisions because of bodily autonomy) for why certain abortions should be legal.

If women should have the right to have abortions because, as pro-choice blogger Amanda Marcotte believes the Supreme Court opined, "Your body belongs to you," then why on should any kind of abortion be restricted? Do the bodies of women who are 8-months-pregnant no longer belong to them? Does a woman lose her rights and her ability to make decisions the moment she enters the third trimester? If not, then why should this kind of abortion be restricted in any way? Why should pro-choicers like Obama need to hide behind this qualifying language of "health?" If pro-choicers believe that a woman owns her own body and can do with it whatever she desires and we should trust her to make the decision, then how can pro-choicers want any kind of restrictions on late-term abortions?

Now, maybe a pro-choicer would argue that late-term abortions are rare and only occur for serious reasons. But this dodges the question. It shouldn't matter if they are rare or not and if they only occur for certain reasons or not. If the reason some pro-choicers believe abortion should be legal is because a woman owns her own body then it follows that those pro-choicers should believe abortion should be unrestricted throughout all of pregnancy.

Others pro-choicers might feel/argue that abortion should be restricted after a certain time period because at that time (be it viability, six months, etc.) the unborn becomes what they consider a person. Notice how this adds a rather large exception to the "Women own their bodies" argument. Now it's "Women own their bodies but can't kill persons even if that person is in their body." Then the question quickly becomes "Who is a person?" and "What's the difference between human beings and persons?"