Many states already do for the most part.

Although people often quote it because it is the seminal case, Roe v. Wade had actually been modified to some extent by subsequent cases such as Planned Parenthood v. Casey. The existing SCOTUS 'line drawn in the sand' for quite some time has been that states can ban abortion once the foetus develops to a state of viability (ability to live outside the womb on its own with assistance) except in cases where the life or health of the mother is at stake. 'Health' has been the sticking point, with the assumption and explanation that is must be a serious health problem rather than a petty one, and obviously both sides look to probe and push the huge grey areas in that exception.

This case involved a specific procedure, and one with unusual aspects. First, it involved late term abortions, an area where the state may generally prohibit them. Second, it involves the partial induced birth of the foetus. Based on medical experts they felt were credible, Congress has taken the position that the procedure is not necessary to save the life or serious health of the mother because full birth can be obtained as safely when looking at partial birth abortion.

They are allowed to make these assumptions and pass laws. When challenged in court, experts were put forth by both sides with each sides' experts saying the procedure was either necessary in some cases or not. But, in such cases, Congress' reliance on the doctors who find that it is not necessary is to be credited unless it is clearly shown to be frivolous, and that could not be done. Mere differences of opinion on the matter are not enough, and Congress gets the deference. The fact that anti-abortion Congresspeople may have credited testimony out of bias is not enough either. The examination is an objective one: is their claim that the procedure is not necessary a legitimate assumption based on medical evidence or is it entirely frivolous and pretextual for an improper purpose? Congress won this debate today that their allegations and reliance on their experts was not frivolous.

To me, this is not the kind of scheme that will lead to overturning SCOTUS protection for abortion procedures. More anti-Roe appointments or a change of opinion on Roe by a sitting Justice can only do that.