American liberals probably received that appellation some time around the First World War (or right before it). The era of Eugene V. Debs, John Reed, Max Eastman and pretty much everyone in the Greenwich Village socialist scene helped to turn people whose thinking was "liberal" or "free" to social causes - unions, anti-war rallies, pushes for full suffrage (women and minorities), temperance, full employment and, in many cases, the implementation of a socialist state. After the Russian Revolution and the Red Scare, someone who advocated full-blown socialism tended to be classified as a "radical", so "liberal" was somewhere closer to the center but still definitely on the left.