There would definitely be more research into methods of birth control, and people would definitely get more responsible with their sexuality. We’ve done it before; we could do it again. Thus, I think there would be fewer unwanted pregnancies. I doubt people currently get pregnant with the intention of having an abortion, but knowing one has insurance does allow one to take some extra risks. Statistically, I see unwanted pregnancies decreasing. After all, this would be much publicized, and I think many would think twice whereas before they would only have thought once.
Perhaps there would be an increase in child abuse. That is a legitimate fear, but understand that the prolifer believes that an abused life is better than a murdered life, and an abused life can be salvaged.
I doubt orphanages would return to the United States. Adoptions would increase, though.
There would be illegal abortions. Heck, we’ve outlawed burglary, and people still do it.
For pro-lifers/anti-abortionists, the rape & incest case is (or should be) a case of whether it is permissible to transfer harm from one innocent party (the mother) to another innocent party (the “baby” – we are talking about this from the pro-life perspective, remember, so I think it is ok to say “baby”).
The only way abortion is a lesser evil than bearing a rape-conceived baby is if you don’t believe the fetus is a human life with a full set of human rights.
Generally, our society tries to right wrongs by making the perpetrator either compensate the victim or otherwise “make the situation right”. But in the case of a rape leading to conception, the situation cannot be made right without involving an innocent third party (again, the baby) who was placed in the situation through no fault of their own.
Also generally, our society frowns upon transferring harm from one innocent party to another innocent party (although in some litigations, that seems to be changing). The innocent party suffering a harm generally must keep the harm if the harm cannot be passed to a more more guilty party (e.g., through fining a criminal, or whatnot).
Thus, in order to justify transferring the harm of the rape from the mother to the baby, one must justify transferring harm from one innocent party to another innocent party. Generally speaking, this would be a deviation from American common law, and if you accept as a given that the fetus is a human life with rights, one could expect an uphill battle to justify abortion in rape cases.
Bottom line, rape and incest are bad acts, and like murder, they are not fixable.
However, given the political realities in America, and the ability of people to ignore difficult issues such as this for expediance and convenience, I would expect that abortion would be allowed in the case of rape or incest if we ever got to the point of banning it.