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I know it's a term that has little history in the US, but with the Repubs throwing "socialist" around at every opportunity, it seems clear that such terms are going to enter the lexicon one way or another.
Unlike "liberal", "progressive" or even "conservative", "social democrat" has a reasonably clear meaning, combining a commitment to personal and political freedom with support for the welfare state and publicly provided services, along with a commitment to government intervention to stabilise the economy. That covers most of the connotations of "liberal" and "progressive" that appeal to supporters of the Democratic Party, without the baggage.