Steve Waldman, the founder of Beliefnet.com, looks seriously at both parties' political positions and success in reducing abortion rates. His conclusions find fault with both approaches--and he suggests cooperation on the mutually acceptable initiatives that would reduce abortion rates. Some of the non-coercive means of reducing abortion--increasing payments for Women, Infants, and Children; improving male employment; sex education (including abstinence education, which could be supported by all faiths) all have been found to reduce abortions.
There is also discussion about how politics often trumps practicality in the pro-life movement. In order to keep the Catholic Church, it opposes contraception. In order to keep the evangelicals, it opposes all types of sex education. In order to keep the conservatives, it alleges that social programs lead to moral decline. The result is that you have a strong pro-life coalition so concerned about keeping all its component groups happy that many initiatives which would greatly reduce abortions are vetoed by one or another of the components.
The impact of overturning Roe v. Wade would not be great.
I would like to see legislators of good faith work together on every aspect of reducing abortion that can be mutually agreed upon. It's a good start, and if they actually did start working together maybe a lot of the wild, mean-spirited accusations that prevail would end as they supported their goal.