But that policy process will have to have its effects through political parties, and that matters. The "primordial soup" of policy ideas that are floating around, waiting for the policy window to open, is not undifferentiated. There are liberal ideas and conservative ideas. Gun control is a liberal idea. Prayer in school or arming teachers are conservative ideas.
Seth has observed, accurately, that the Democratic Party had more or less given up on gun control in recent years. That's definitely true. And on that criterion, it's reasonable to say that the Democratic Party was no longer really "for" gun control.
But liberals most certainly are. There is a difference between an ideology and a party. A party is an institution that tries to win office and push for policy. An ideology is a more abstract set of preferences about policies, tied together by a mixture of principles, values and beliefs.
Today, the liberal ideology is associated with the Democrats, and so if the policy window opens on gun policy, it will be Democrats who will be responsive to liberal policy pushes. The kind of sustained pressure to shape the party that Seth wrote about may be needed, but this party is predisposed to listen to liberal ideas, and Democrats -- even those already in office -- may actually be quite responsive to pressure. Meanwhile, Republicans have a similar relationship with conservatives, who oppose gun control, and would favor other solutions.
So which solution wins depends a lot on who is in power. And since we have divided government, it is unlikely that only one solution, or one side's solutions, will be heard. If any legislation, on gun control or anything else, passes, it really will pass through the gauntlet of both parties, and probably involve a mixture of policy ideas.
Or, more likely, nothing significant passes.