I am well aware of the reasons why it didn't get through. The median voter doesn't. Saying you will do the same means you will do the same, ie, it will be blocked somehow.
By the way, it's not true that it was entirely stopped by Republicans - for every vote there were Democrats that went over the line, and the Democratic leadership failed to whip or primary them, which the voters rightly or wrongly will assigned the blame for the Democratic party.
Additionally, the fact that Trump appointed judges that were able to block them is in no small part thanks to the Democratic party being too ineffectual to do the same in the Obama and Biden administration.
Unless the Democrats make a point of recognizing what they could have done to play the game better and get their campaign promises through, the average voter will, rightly or wrongly, simply interpret this as the Democrats not being willing or able to follow through, and penalize them in consequence. When the Democrats willingly slow down and let internecine fights prevent themselves from helping people while the Republicans just ram their agenda through, voters will inevitably interpret this as the Democratic party making the conscious decision to break their promises, which is not entirely correct but not entirely false either.
To avoid this, Democrats would have had to be candid and say that they would likely not pass their electoral promises even if they had a majority (see: Obamacare), or somehow fix their party and get their shit together.