If the US is going to permanently annex the CS (and it looks like they did) how will they handle the reintegration? How would they deal with convincing the Confederates that being citizens of the US was good and desirable? How would they eliminiate nationalist feeling in the old Confederacy? From the books it looks like the US was employing draconian measures. They cannot keep that up forever.
It strikes me that aside from the military occupation, Morrell's Equality pamphlet (along with other such means) are an effective way of swaying Southerners into accepting that the United States is here to stay (among other ideas). In short, Southerners might not like the situation, but the vast majority realize that nothing can be done about it.
There will also not be the sort of massive revolt seen in former Canada and from the Mormons on the part of the Southerners. Even after twenty years since the end of the Second Great War, they remain too weary to even contemplate launching an uprising.
The upcoming generations of Southerners will increasingly see themselves as "Americans," along with everyone else in the Union.