I've definitely taken preference to the term leftist or progressive over "liberal"... I don't think the modern left could be described as liberal in any classic sense of the term. That said, I don't think many on the left are particularly progressive either.
Do you believe our society should value tradition and hierarchy?
Yes -> right-leaning
No -> left-leaning
"Progress" implies there is an inevitable way forward, for which other beliefs are leading society astray from.
When it comes to things like "Are you prejudiced against groups of people?" the progressive answer is always "no". People on both "sides" can find valid reasons to say "no" to this question, but it's hard to maintain an internally consistent worldview if you're left-leaning (oppose hierarchies) and still want others to be lesser (which requires a hierarchy). Mainstream racism, homophobia, etc. naturally concentrate on the political right, but up until a few years ago, opposition to same-sex marriage was a mainstream position for liberal Democrats, too.
This is all to say, there is no actual significant leftist representation in American politics.
