Their largest vote total was received prior to World War I.  Resistance to the US involvement in WW I, the Palmer Red Raids, and internal split on Bolshevik Revolution reduced them to insignificance as a party.

Thank you for adding crucial historical benchmarks and qualification of party "significance" restricted to votes. But is that really an appropriate measure of the party's influence on "national policy"?

I would think the continuity of US federal law and police actions to destroy this (third) party's apparatus and political alliances across the labor movement was a significant feature of national policy.  

If not, I still must wonder about the popularity of socialism within FDR's administration and right up to the end of WWII, while Russia enjoined favored nation status. Wilkie's "One World" tour was quite the money-maker, no?

Diversity is the key to economic and political evolution.