The situation has some similarity to the New Deal. Following Democratic wins in 1932, the Democratic party faced an internal challenge: how progressive did it want to be, and did third party such as the Socialist party offer viable alternatives. Roosevelt was able to stave off significant losses in 1934 by embracing some of the more progressive policies of Huey Long, who continued to pressure Roosevelt from the left until his assassination in 1935.
Here, the current economic and social crises, combined with the ability of the Internet to harness people in collective action, is giving rise to extremely well-organized and well-funded movements in both parties. This is not necessarily a bad thing, given my personal political proclivities.