You have noticed something pretty significant here.
I would suggest that the situation has more depth to it than you suggest. You say one side "does nothing" while the opponents "set the narrative." It appears to me that what underlies the situation you describe is something like this (I am trying to describe, not judge, to the extent that my limited abilities permit):
The conservatives take their opponents seriously. They acknowledge that their opponents have valid points, and many times they say to undecided / independent voters, "I can see how you might be tempted to think that way. We've examined that point of view, and here is where we find it lacking, and here is what we offer instead, and here is why we think you should choose our option instead of their option."
The progressives seem to be convinced that they are morally superior. They assume without providing justification that they are "right." They denigrate their opponents as "selfish" or "heartless" or "uncaring" or "stupid"* or "evil." They don't even respond to their opponents (look at the response from the progressives when it was first suggested that PPACA might be unconstitutional...bascially, it was a snort and a dismissive wave, no?).
Now, you call the former "setting the narrative" while you call the latter "doing nothing." Those labels also fit the narrative I describe.
Let's pretend we are undecided for a moment, not affiliated with either side. One side seriously tries to engage me in a dialog, the other side projects moral superiority and contempt for anyone who disagrees and offers no serious justification for their viewpoint. Regardless of what you personally believe to be the relative merits of either side, which approach do you think most people would find more congenial to being persuaded?
*(how much vitriol have we seen here directed at people who "get their opinions from Fox News"? how persuasive is it in a conversation to tell the other person, "I'm going to stick my fingers in my ears and start humming so that I don't have to listen to what you have to say." ? how receptive am I going to be, if I present for consideration information I've heard or read, for the other person to call me a liar unless I provide justification?)