They don't seem to be trying. Why don't I hear Democrats talking endlessly about how irresponsible it is of the Republican's to hold the country hostage by politicizing about the debt limit? To do so would require a bit of explanation. The Republicans have apparently convinced the public that not raising the debt limit is a good idea. And the Democrats are too politically incompetent to dispute that.
People are swayed by demagoguery, but they are also at least somewhat open to intelligent views. The Democrats should at least try it. They will never out demagogue the Republicans, so why not establish themselves as the party of clear thinking adults. There must be some sort of constituency for that.