It most certainly would happen in most, perhaps all, blue states. Overturning Roe vs. Wade means that pre-existing state law takes over, and at least one state I know of (WA) passed an initiative to liberalize its on-the-books abortion law in the eventuality that an overturn occurred.
However, much, perhaps most, of the country would not liberalize abortion to the extent that it exists today. Frankly, during an election year, I'd prefer that Scalia remain silent about abortion except if he's part of a binding decision on the subject.
Coward.