Again, in response to E$.
I did a quick, therefore inadequate, search of the state of abortion laws at the time Roe was decided. I believe (this is in part from Blackmun's opinion) that at least 18 states allowed abortions under similar statutes to this:
Justifiable Abortion. A licensed physician is justified in terminating a pregnancy if he believes there is substantial risk that continuance of the pregnancy would gravely impair the physical or mental health of the mother or that the child would be born with grave physical or mental defect, or that the pregnancy resulted from rape, incest, or other felonious intercourse. All illicit intercourse with a girl below the age of 16 shall be deemed felonious for purposes of this subsection. (this was the Model Penal Code's version at the time)
Obviously abortion was more restricted prior to Roe, but it was certainly not proscribed everywhere. It was allowed before the 26th week of pregnancy in these states where it was not proscribed. The interpretation of the statute worked much like abortion statutes now, under much judicial interpretation of "physical or mental health of the mother". It was probably not as liberally condoned by courts as it is now under the Supreme Court's (lack of) guidance a la Roe and Casey, etc. especially in say, Arkansas (where it was legal), and it might have been just as liberally condoned in more liberal states. I do not know.
I think pro-abortion people have not pushed for legislation for multiple reasons. It is very unlikely the Court will overturn abortion case precedents altogether. If it does, then advocates can enact liberal abortion laws if they are able. I think many states would allow abortion if this were to happen, even more liberally than in 1973.
Secondly, abortion liberalization statutes would undermine pro-abortion court rulings. The core of Roe was that women had a 'fundamental right' (a very loose constitutional term of art) to abort. Thus, in most respects, it is beyond the powers of legislatures to touch. Such legislation would be an admission that abortion decisions rest on shaky foundations. Incidentally, due to the politicization of the issue, those shaky foundations are less freely admitted now than when Roe was written. Abortion rights advocates cling to that ruling despite its treatment in Casey and by liberal legal scholars after Roe was written.
Finally, related to the first two points, for better or (more likely) for worse, we believe the Supreme Court is the final--and in most respects--only arbiter of Constitutionality. This serves to devalue legislative and executive pronouncements. We have come to the point where Congress and the President sign and pass things they themselves might believe unconstitutional and say, "the Court will deal with it". Thus elected officials don't have to take unpopular stands in defense of the Constitution anymore. They just push it off to the courts. Can you imagine a President, a la Jackson or Lincoln, openly disobeying or even roundly criticizing the Supreme Court? It is nearly unheard of in our time.