The Supreme Court has granted cert in a Mississippi case which provides a clear vehicle for overturning Roe v. Wade.
So how doomed is Roe? Answer: Pretty doomed! There are essentially two possibilities for what the Court will do. One is that Roe is overturned, simple as that. It's easy to find at least five votes for that position, and the current generation of conservative jurists view not just Roe but Casey as a political betrayal. So that has to be the front-runner out of the gate.
The second possibility is that Roe dies in life -- nominally "upheld", but in such a minimalistic and strangled form that it effectively does nothing. Mississippi's law bans abortions at 15 weeks; if it strikes you as impossible to uphold that law and say you're not overturning Roe, take a look at what the Court just did with its juvenile life-without-parole precedents. As I've said on many occasions, this is a John Roberts special -- he'll maim precedents and then brag about not killing them. But Roberts now is only the fourth vote on the Court, so the question is who could he even bring along to fulfill this charade? Kavanaugh? Gorsuch? Barrett? It sure as hell won't be Thomas or Alito.
If you asked me to put numbers on it, I'd say the probability of Roe being overturned outright is over 50%, and the probability of it being either overturned or neutered beyond recognition is over 90%. The likelihood of even preserving the Casey status quo is close to negligible.