There was going to be a USA after the Civil War ended. That is a fact. At worse the USA was fighting for stalemate, at best they conquered the South. At best the CSA was fighting for existence and at worst case; annihilation. There was no threat to the USA sans the south. The existence of USA was not threatened by the Civil War. The union between the north and the south was at stake but not the USA’s existence.
In fact, as DiogenesLamp happily points out, had Confederates won they would have strong claims to states like Illinois, Indiana & Iowa whose exports shipped down the Mississippi to New Orleans.
Washington. DC, itself could become the Confederate capital, surrounded by Confederate states.
The rump US capital would once again flee north, to Philadelphia or New York.
So North America would split up into its several constituent parts and the United States would be no more: