Question: Are pro-choicers confident enough in their position to support individual states deciding how to handle abortion?
In the August/September issue of libertarian Reason magazine, senior editor Radley Balko analyzes how the U.S. Supreme Court wresting the decision from Americans was a bad legal decision that resulted in chaos.
Balko first runs through an interesting list of some who think the Roe v. Wade decision was poor:

In 1985 a prominent liberal legal figure argued that Roe v. Wade, the Supreme Court decision that established a constitutional right to an abortion, was a “heavy-handed judicial intervention” that “was difficult to justify and appears to have provoked, not resolved, conflict.” The writer was Ruth Bader Ginsburg, now an associate justice on the U.S. Supreme Court – and also now a strong supporter of Roe.
Ginsburg isn’t the only backer of abortion rights to have taken issue with the 1973 decision. In 1995, for example, the University of Chicago’s Cass Sunstein, a superstar among liberal law professors, wrote in the Harvard Law Review that the high court “should have allowed the democratic processes of the states to adapt and to generate sensible solutions that might not occur to a set of judges.”….
Pro-choicers who have recently criticized Roe v. Wade include The Washington Post’s Benjamin Wittes and Richard Cohen, Harvard’s Alan Dershowitz, and Slate’s William Saletan.

Balko explains how the Roe decision resulted in chaos….

Roe, [Sunstein] argued, centralized an issue centered around privacy, reproduction, and medical ethics, all matters that traditionally have been the province of the states. Moving those moral debates to Washington forced a one-size-fits-all policy on the entire country, raising the stakes, and therefore the contentiousness, of an already divisive issue….
The main difference between a purely federalist approach to abortion and what we have today is that in the former each side wouldn’t be clamoring to control the federal government so it could impose its favored policies on the rest of the country. The battles would be fought in the state legislatures, and national politics would no longer be held hostage to the abortion issue.

Balko says the Roe decision actually interrupted pro-abort momentum; it was swinging their way before the Supremes intervened. Conservatives were frogs in a pot, basically.
Clarke Forsythe of American United for Life has made the case that the abortion movement had stalled by 1973.
Either way the Roe decision polarized America. Forsythe says it galvanized pro-lifers; Balko says it galvanized pro-aborts.
Balko seems to think we’d be in about the same place anyway – same numbers of abortions, same laws, just a lot less poison in the air:

[W]hile overturning Roe would represent a political victory for pro-lifers, the reversal wouldn’t necessarily prevent many abortions. The pro-choicers achieved enormous momentum in the ’60s and ’70s, and support for reproductive rights is much stronger today than it was before Roe.

As late as 1967, 49 of the 50 states still made it a felony to provide an abortion. But in June of that year, the American Medical Association passed a resolution reversing its prior opposition to abortion in cases of rape or incest, severe physical deformity of the fetus, or danger to the health or life of the mother. That started a sea change in state legislatures. By the time Roe came down in 1973, just six years later, 17 states had legalized abortions performed to preserve the life or health of the mother. Colorado, North Carolina, and California also included exceptions for the mother’s mental health. Alaska, Hawaii, Washington, and, most significantly, New York had passed laws essentially guaranteeing abortion on demand….
Without Roe, the pro-choice movement would have had to keep taking its case to the state legislatures. States with more permissive attitudes about sex and reproductive rights likely would have passed more permissive abortion laws. Other states would have embraced tighter restrictions. And some states would have kept the existing prohibitions in place.
Had Roe gone the other way, it’s likely that “partial-birth” abortions already would have been prohibited in most states…. States with a strong interest in preserving parental rights likely would have required parental permission for a minor to obtain an abortion. Some states might allow abortion but prevent the use of public funds to pay for the procedure. Others might allow abortion on demand and provide funds to ensure poor women’s access to the procedure.

And here’s how local control would undo legalized abortion. Explains Balko:

A new book by a staunch critic of abortion also suggests a decentralized approach. In The Politics of Abortion, the conservative sociologist Anne Hendershott offers a scathing, unabashedly polemical history of the pro-choice movement….
[S]he closes the book by calling not for more federal antiabortion laws but for returning the issue to the states. It is time to end the “superficial slogans that rally the troops but build impenetrable barriers,” she writes. “Taking the discussions out of the courts and back to the realm of local policy, where we might once again debate the politics of abortion as neighbors and friends, would be a good start.”
On that much, at least, she’s correct. The “pro-choice”/”pro-life” split suggests that only two options are on the table, when in fact far more positions are possible….
Most views, of course, lie somewhere in between, offering different perspectives on everything from when human life begins to who, aside from the mother, might have a say in the decision to end a pregnancy.
Abortion policy, then, is about drawing lines and setting community standards. Such issues are best dealt with in those diverse laboratories of democracy, the states. A federalist approach would allow a wide array of abortion policies that better reflects the spectrum of public opinion on the issue. That isn’t to say a federalist approach would leave everybody fully satisfied. There would still be people stuck in states whose laws don’t reflect their personal values. But that much isn’t very different from the way things stand today. Roe prevents any state from banning abortion outright, but in places like Utah and Mississippi abortion is extremely rare, due not just to legal restrictions – waiting periods, mandatory counseling, parental notification – but also to the fact that prevailing community values mean there isn’t much of a market for the procedure. Mississippi has just one abortion clinic in the entire state.