US democrats are the largest and most successful left party in the world. Our large two party system obfuscates the underlying factionalism within the political parties (progressive cacucus, justice democrats, blue dogs, New Democrat Caucus) kind of reveals this inherent disagreement within our political parties, where members of the progressive caucus and justice democrats can be pretty clearly seen as on the political left.
In the US, social liberalism and political freedom is generally much more popular, as compared to Europe, and seen as being associated with the political left. There is no major socialist political group in the United States, and usually people who claim that there is "no left wing party in the US" want an actual Socialist party, but there are very few examples of successful socialist parties in Western Democracies and tend to be consigned to either being permanent opposition, or forcing themselves to liberalize to the point of not being socialist anymore (think SPD in Germany and Labour in the UK).
I am thankful that the US democrats focus so strongly on issues of social liberalism, think, immigration, abortion, LGBTQ rights, where in Europe these issues are much more controversial especially on issues of abortion and immigration.