The Centrist Independent Voter policy position on abortion rights is that if Roe/Casey is overturned, we should attempt to re-establish those same rights legislatively. The position is also that we should not take that opportunity to either expand or contract those rights.
Susan Collins(R) and Lisa Murkowski (R) have jointly introduced legislation in the Senate to accomplish exactly this objective. This link also provides their defense of this legislation.
If the Democrats in the Senate were to embrace this proposal, they might well be able to muster the votes necessary to overcome the filibuster. In addition to Collins and Murkowski, Shelley Moore Capito (R) is pro-choice. I believe seven more Republicans can be found who would settle for this legislation rather than risk having the Senate rules changed to eliminate the filibuster and seeing the Democratic version of this legislation pass and seeing the Court packed with liberal justices.
Remember some conservatives objected to the Roe decision because it represented an overreach by an activist court rather than because of the content of the decision. Reversal of Roe combined with a legislative answer to the issue constitutes victory for these judicial conservatives.
Democrats who want to use this issue to end the filibuster and pack the Court should remember that they will not always be in control.
Democrats who turn down this compromise, because they hope to gain a political advantage in the mid-terms, should remember that their refusal to even consider the compromise will hurt them. They should also remember that while support for abortion rights similar to those laid out in the Collins/Murkowski legislation is widespread, support for unlimited abortion rights is far less popular.
A final reason for Democrats to embrace the Collins/Murkowski bill is that it would make a Supreme Court decision on the issue currently before the court moot. If the Collins/Murkowski bill became law, the Mississippi law before the Court would clearly be illegal. The Court does not issue decisions if the issue is moot. That would address the concern that the Alito draft decision, if adopted, would set a precedent that would undermine other court decisions such as contraception and same sex marriage rights. If the Democrats wait until the Supreme Court delivers their final decision they will have missed this opportunity.