The Democrats have rarely had a filibuster-proof majority in congress that would allow them to codify Roe. And they have been working under the assumption that it was a settled issue. As I recall, even some of the recently appointed Supreme Court justices were under that impression as well. At least until they were sworn in.
Even when they had a filibuster-proof majority, they didn't have a majority that believed in abortion rights. Some of the democrats in obama's brief filibuster proof session were pro life. Even now, at least 1 democrat senator is pro life.