I've pointed this out in the past, but it bears repeating: I really, really don't like using the word "progressive" instead of the word "liberal".
To begin with, progressive has all kinds of historical contexts that liberal doesn't, and many of them are very nasty. The American Progressive movement of the early 20th century had a few good elements, some bad ones, and some really deeply noxious ones. We don't need those kinds of associations. (To those who say that conventional American liberalism is a straight descendant of the Progressive movement... no.) Liberal, in contrast, is a great word with an almost totally proud history. In fact, many conservatives say that the American conservative project is really the classic liberal project.
What's more, not standing up for the term that you self-identify with is precisely the kind of retreat and weakness that we have been tarred with for years. Do you think even now, at a moment of great defeat for their movement, conservatives are going to give up the term "conservative"? Of course not. Conservatives fight for their self-identification. Sometimes, this has negative consequences for conservatism. The refusal to genuinely reassess priorities and the penchant for cultural war, I believe, are consequences of this same kind of thinking. But politics ain't beanbag, like the man said, and if we are resigned to a politics of pugilism (the only kind), then we should be willing to fight for our symbols and our nomenclature. Liberal is a good word, and worth fighting for.