The position that a woman who was impregnated due to rape should be forced to carry that child to term is an extreme position. Very few politicians openly espouse this view.
The differing status of these two positions helps us to see the hidden motivations behind the anti-choice agenda: punishing sex. Personally, I don't think that this is the thought process of people who are anti-choice. Rather, I think the anti-sex culture leads to a certain mindset, which leads to certain positions, and those positions are then justified in the mind of the holder.
For the anti-choice crowd the justification is a simple equation:
Life of 'child' > 9 months of mother's time/effort + adoption proceeding
That's the simple equation that is trotted out. Life over short term loss of liberty. Smart liberals even buy into this equation (myself included). We say 'I don't believe that a fetus early during pregnancy is a life, but I think that's an understandable position.' In this way, we accept that this equation is the reason someone is anti-choice, rather than just an after the fact justification.
So lets look at the equation in the situation of a rape. The equation doesn't change. If you believe a fetus is a 'child' then an abortion is still murder. The nature of the events that created that fetus have no bearing on this position. Yet many people who claim to be motivated by this equation would consider a rape exception to be obviously required.
The reality is that pregnancy is a primary 'consequence' of sex. It's used to frighten teenagers into not having sex, along with STD's and getting a bad reputation. Safe, legal abortions threaten to take that consequence away, and we all know that evil deeds should have serious consequences.
When a woman is pregnant, ultimately the anti-choice crowd views it as her fault. She did this to herself. It doesn't matter if she used birth control like the pill or condoms (or if she took abstinence only education: chewed spearmint gum and did it standing up), she is guilty of getting laid. If she didn't want to be pregnant, she shouldn't have had dirty dirty sex. The pregnancy, the adoption, the government telling her what she now cannot do with her body, is the consequence of her wrong action.
But when a woman is raped, none of that feels right. It's not her fault. So the underlying anti-sex motivations aren't there. Despite the fact that it's still a life, despite the fact that it's still 9 months of her liberty at stake, still a lifetime of having a child, the situation has changed. It's changed because she doesn't need to be punished for having sex. In that way the rape exception just makes sense to many anti-choicers, even if they would have a hard time articulating why.
This exact pattern is evident in refusal to support Plan B, while supporting in vitro fertilization that requires the disposal of fertilized eggs. It isn't about life, it's about not letting people get out of the consequences of their dirty dirty sex.
By wrapping itself in 'protection of life' the anti-choice group is the most powerful wing of the anti-sex section of our culture.
P.S. In fairness, there seem to be an increasing number of people who oppose the rape exception for abortion bans. See here. But it's still a minority position among anti-choicers, and another topic entirely.
P.P.S. While I'm on the topic. Can we dispel the whole 'if abortion had been legal, my mom would have aborted me. Do you want me to be dead?' argument. How many people are the result of broken condoms? or failed birth control? of power outages? If I was conceived during a power outage would it make sense for me to oppose a better power grid? "If these redundant power lines had existed 29 years ago I never would have been born, do you wish I was dead?" There are a lots of circumstances that line up to result in a human being of adult age. The 'I wouldn't be here' argument is an intentional distraction from any real discussion of policy implications.