The United States has a functioning government capable of command and conscripted soldiers bursting out of their asshole. Let us not forget that over the course of the OTL ACW, the Union fielded over a million troops. Things are rough, yes. It would definitely be in their best interests to settle up. But they aren't out of the fight, and it is not inconceivable that, if they chose to push on, they could win.

And yes, rolls can *always* be that bad.