Most of the American left is in fact unified - behind the Democratic Party.
No, quite the opposite. The Democratic Party's strategy is to appeal to leftist unity only when it's time for elections, only for them to give no concession whatsoever and keep on their neoliberal agenda.
And they're not on the left to begin with, they're right-wing. Them being leftists is only an illusion caused by the Overton Window.