This is a really excellent book about, well, literally, the fall of Roe.
One of the points they make is that for years and years leading up to the overturning, the Democrats focussed on winning hearts and minds and the right wing Republicans focussed on the stepping stones of creating court cases and and judge shopping and creating Supreme Court judges.
There was good reason to believe that although the law behind Roe wasn't as watertight as people would have liked, it was settled. Until Supreme Court nominees came along who were willing to perjure themselves about stare decisis during their confirmation hearings, it wasn't that big an issue.
Obama had a very short time where he could have done it and he was kind of busy proving to the country that he wasn't a radical muslim sent to bring down the country. He was sometimes too careful for my liking, but I think codifying Roe during the 90ish days where he could potentially have done it would have been an extremely politically destructive act. Plus, they were focussed on the healthcare battle at the time, which was insanely difficult.
Sorry - adding link to the book
https://www.thefallofroe.com