The people that stand to lose the most from this is women. While I believe that men should have the right to revoke parental and financial liability prior to a child's birth since we don't have the right to force an abortion, I also believe its plenty of women that would be screwed over by this decision as well. I don't feel like writing up a full bill of how a law like this would work but I can't see how, while it would be fair, this wouldn't cause alot of men to bow out of responsibility after something like this is enacted. The goal of a law like this is not to give men more rights then we deserve but to cement a woman's right to choose what she wishes to do with her body.
A woman can have an abortion up until the end of her first trimester. She has less than 12 weeks to make a decision and less if she finds out late. That's also enough time for a man to know if he wants to take responsibility or bounce and pretend it didn't happen. If a woman has to choose between being a single mother or having an abortion, that decision won't be an easy one to make. In this picture, men hold all the power while a woman has to make a life altering choice that affects two people. If we're going to allow men to knock a chick up and absolve himself of responsibility then the least we can do is give women the power to decide if they want to allow a situation like that to happen.
As someone said earlier, this would be an easier conversation if women didn't have to carry a child for nine months but this ain't that. As it currently stands, its easier to just not nut in a woman you don't want kids with than to go this route. This is closer to a divorce without even getting married.