I believe many pro-lifers would be satisfied with the prospect that some other states make abortion legal so long as their own state bans it. This would include pro-lifers who recognize that the Constitution is silent on the topic of abortion, so no branch of the federal government is delegated the power to ban abortion across the entire nation.
This was my initial thinking on this subject as well, but I'm not sure I believe it anymore. If someone genuinely believes abortion is child murder, why should they be satisfied with a situation where babies are being killed in California but not Tennessee?
This relates to something that I think foreigners have a hard time understanding about American politics. More than once I've seen someone comment that the anti-abortion side is winning because abortion rates are going down in America, which is just an absolute misunderstanding of the actual issue. It's not a matter of one side wanting more abortions and the other wanting fewer abortions; given the belief that abortion constitutes murder, any legal abortion is too many.