I feel like making my prediction publicly, even though I think nobody's paying attention. It'll be archived so that I can say I was right. Or (I hope!) wrong.
Roe v. Wade is close to settled law. It will not be overturned directly. Instead, conditions must be created to change the assumptions, so that it is conspicuously in error.
The key assumption that will be changed is whether or not the fetus has rights. I forsee the Roberts, Scalia, Thomas and Alito block setting precedents for fetal rights. At some point, after fetal rights are firmly established in a variety of cases, Roe v. Wade will be found in error because fetal rights conflict with (and outweigh) the woman's rights.
First attempts along the lines of fetal rights have already taken place, both in the courts and in legislatures.
All that's needed is one more anti-abortion vote on the court. They will find for fetal rights, and then "regretfully" have to overturn supreme court precedent.