As a monarchist and a big-state skeptic, I should be one of them, if people fit simple patterns.
But I think the US is cohesive enough to hold together, barring something breaking that.
Which is to say, there would have to be a pretty powerful force working to undermine it. Even the OTL ACW would only cut in two very uneven pieces (if the Union failed), not leave it splintered like what had been Austria-Hungary before 1918.
That might happen from some particularly nasty string of events, but I wouldn't count on it.
There's just not a lot of reason to break it up - especially when there's no "_____ fighting for ____'s wars." sort of thing that would divide Germany and Italy (not necessarily disunite, but certainly cause friction) in even the best HRE scenario, for instance.
So barring slavery, what else is there? The West may be hostile towards the East, but that's not something that would be better with the Midwest as an independent country - in all ways it would be worse to deal with a foreign power in that position.
And a civil war in the sense of trying to take over the government in the classic sense...the US's republicanism was not oligarchical enough for that. Not truly democratic for some time, but socially sufficiently supportive of anyone with the will and luck succeeding (or just about anyone) to undermine that.
Looking at the country on the whole, obviously.