Apparently we've reached a point where the term "socialized medicine" actually polls well. See Ezra Klein for further discussion. I would only note that the leading Democratic candidates are not, in fact, proposing to deliver medical services on a socialized (i.e., public sector) basis. Nor are they really proposing to deliver health insurance on a public sector basis (the way Medicare works).
Which is all too bad, because socialized medicine is, in my view, a good idea. Democrats have various reasons for not putting actual socialized medicine proposals on the table, but at least one reason is a desire to rebut the charge that they favor "socialized medicine." But if "socialized medicine" sounds good to people, then they may as well propose it.