What does left-wing mean?
http://en.wikipedia.org/wiki/Left-wing_politicshttp://en.wikipedia.org/wiki/Centre-leftFrom people who say the Democrats aren't, I get the vibe they usually mean something along the lines of supporting a European-style welfare state, because apparently European politics and economics is now the golden standard to which all political parties around the world must be held against (Euro-centrism is getting old, and this comparison is really stupid especially when you've got parties that could be considered left wing on economics but socially conservative and hate gays, abortion, and immigrants, which is something I must've missed at the DNC convention in 2012).
They're just mad that the Democrats occasionally have to compromise in our two-party system, and aren't more aggressive in pushing for more government intervention, if not outright democratic socialism.
They're a center-left party, so yes, they're left-wing.