Going to cheat a little bit here. Because since North and South Carolina were colonies well before the revolution, they aren't really States per se. But we can have them united.
In a more radical civil war, we have South Carolina getting the brunt of things as a lot of Confederate holdouts go there for some final Titanic battles. Destruction is even greater there. The state is well over 70% Black by the end of the war and there is concern that an utter lack of able-bodied males will mean the state exists in tatters if anything, unless it is made to be a Haven for the freedmen.
Reconstruction is not popular enough after a while, but various things cause South Carolina to be destroyed even more by wandering vigilantes. There is concern that some of them may actually take over the state via military coup.
But, the federal government has one option. North Carolina has a decent government which would be willing to take in the southerners. A referendum is held among white voters and they agree, in return for laying down their arms, to let the state be governed by North Carolina and merge into it rather than allow the federal government to come in and enforce any kind of civil rights.
The federal government's tiredly goes along with this because reconstruction really is costly and they realize the sinkhole that South Carolina has become.
Likely? No. But perhaps remotely possible where South Carolina has been much, much more devastated.
This could even tie in with Virginia not joining the Confederacy. The slaveholders become the ones who form the rebel government and when they are crushed the free Virginia government winds up forcing them back into virginia, with rule of Virginia becoming much more favorable to the Western counties. Perhaps even a move of the capital although that is less likely. (if you need the Civil War to go on for about as long anyway, just have Kentucky secede while Virginia does not.)
From there, Simply have the Dakota's become one state because the federal government, with all this craziness in the south, is too worn out and gives the native tribes some large reservations in Dakota territory with the entire state joining as one rather than seeing two states with a lot of Native Americans in them.