Hard to say. I think the most cliche scenario is a viable, enduring socialist or progressive party emerging in the 1910s and taking the place of one of the Republicans or Democrats (like Labour), or becoming a very strong third party like the NDP in Canada (more likely). You could also see a Dixiecrat Party emerging in the 1950s, which could result in a nightmarish America where an anti-civil rights party holds the balance of power after every election.
I don't know if there's a political science explanation for why some countries with proportional representation only end up as essentially two/two and a half systems parties (like Germany) while others (like Israel or the Scandinavian countries) have many smaller parties that form large coalitions. But, intuitively at least, I feel like America would be more like Germany, with a large center-left party, a large center-right party, and then 2-3 smaller parties.
Basically, we would have a permanent TEA Party and a permanent Green Party that form coalitions with the Dems or the GOP (which will probably be where they were in the 70s).
