"People's Republic of America" sounds weird, and we did already have a Republican party that turned racist. Perhaps the People's Democrats? We've never had a Democratic party before.
Isn't "People's Republic of America" what you guys are shooting for anyway? I think the name would add some badassery to your guys' side of the aisle at least (in a sort of subtle way, IMO). People's Democrats could work, though I fear if you isolated it only to the term "Democrats", we'd end up in 2016 with the exact same left-wing party we have today (albeit, a few more points off-center, but you get the idea).