This is a question I couldn't fathom for a long time myself. I think most Americans have a deep sense of personal responsibility. On one level we balk at anyone being irresponsible enough to allow themselves to get to this position. I think the late-term abortion compromise is a bridge between the two sides for that reason. And, honestly, I don't have a great deal of problem with it.
There are a number of factors that lead to this place. Some are accidental. Not all women exhibit obvious signs of pregnancy in the early stages and still others have such irregular cycles and issues that it's hard to say. Still others are obviously personal responsibility issues that stem from basic denial to social fear, etc. These are the types of factors that we, hopefully, can address through education and prevention along with a reverse stigmatizing of sex (and the role women play in society) in general.
However, it should also be noted that one sneaky element of the right-wing anti-abortion agenda has been to underhand in trying to cir vent the attempt to ban abortion and has been content to simply trick women into carrying to term too late to do anything. The most overt tactic is the false abortion clinic. These types of centers, which have been popping up advertise and claim to be abortion clinics. When women go in, they are inundated with one-sided medical advice and literature, all aimed at adoption. If this strong-arm tactic doesn't work, in some extreme cases these "clinics" have pretended to set and cancel and re-schedule procedure dates until such time as the woman is beyond the legal stage to have an abortion. Before some people in this thread start drooling and ranting about this being just a few cases, I will reiterate that this isn't a huge phenomenon. But it does happen, has been happening more and more in the last 8 years, and should be noted.
The less overt action, of course, is by cutting the funding for low-income clinics that depend on partial funding from the government. Poor clinics can't perform abortions, the cost of abortion goes up and it's harder for low-income persons to get abortions in the early stages since they have to save money for the procedure.
A final element that should not be overlooked is the individual coming to terms with their own personal beliefs. Most people think of abortion in abstract terms, but they don't really know for sure what they believe for themselves until they sit down and face it themselves. I don't think any of us argue that it's a decission that no one should take lightly and should take their time coming to terms with. Often just a couple weeks isn't enough time for individuals. I know this is another personal responsibility issue, but it is a significant enough one to stand on its own in my opinion.
I think this issue, however, is really only relevant as a means to target the need for prevention and education. Otherwise you get into the dangerous waters of "you get what you deserve."