WASHINGTON—On the eve of a critical Senate hearing that could decide the fate of Supreme Court nominee Brett Kavanaugh, a third woman came forward to accuse him of sexual misconduct in the early 1980s as partisan anger deepened on both sides. The revelations shocked Capitol Hill, where Republican lawmakers are seeking to advance a nomination that legal scholars and lawmakers have said could cement a conservative majority. Judge Kavanaugh’s judicial elevation, once expected to move smoothly through the Senate, now hangs on the votes of a handful of GOP senators who said they were troubled by the late-breaking claims. Sens....