The Democrats could have passed a bill, but “enshrining it in the Constitution” would mean passing a Constitutional amendment. First, they would need a 2/3rds vote of Congress. That means that the Democrats couldn’t have a slim majority - they’d need a large majority. Or they’d need to find Republicans willing to vote for a Constitutional amendment protecting abortion rights. Basically an impossibility.
Even if the Democrats managed to get the Constitutional Right To Abortion passed, they would need to have 75% of the state legislatures pass it. Democrats don’t control that name state legislatures.
So perhaps the Democrats could have passed a national law, right? Except that the Republicans would inevitably filibuster this in the Senate. The Democrats could have changed the filibuster rules, but not all of them supported changing these rules. (Mainly because it would prevent them from stopping the Republicans if the Republicans regained the Senate.) Any law that was passed would inevitably have been challenged up to the conservative Supreme Court.
You could definitely criticize the Democrats for not pushing harder to pass a law guaranteeing abortion, but a Constitutional Amendment was out of reach.