I do think there's a fascinating cultural what if there- how does a mid 19thC balkanisation get treated by intellectuals?
So one of the lesser known things about the Imperial Federation movement- a movement, to be clear, that never had any serious traction- was that you often had invocations of Germany and Italy. Just as the late nineteenth and early twentieth centuries were a moment where you had quite serious invocations of international politics as a social darwinian state, where weak nations would be pulled down and swallowed by the victors, you also had a sense that now at last disparate peoples were fulfilling their destinies and coming together.
I think there's even a loose parallel to the kleindeutschland (Britain's empire unifies) and the grossdeutchland model (as above, with America!)
What happens to the intelligentsia of the English speaking world if the United States disintegrates? Does this mean that the 'Anglo-Saxon Race' was somehow older and more tired, falling apart when other nations were coming together? Whose fault was it?* Is there some golden opportunity for Britain to persuade some of her lost colonies to rejoin the fold?**
For America's part, what's the lesson? That the experiment in democracy doesn't work? Or that they were betrayed by planter aristocrats?
You might even see a tendency towards greater centralisation of the Empire in response, though I've always believed that would strengthen the centrifugal forces that broke up Britain's empire, not weaken them.
It's not without the realms of possibility that you see Filibusters within what we think of as America, people dreaming of themselves as Garibaldi, out to bring the nation back together- John Brown, maybe?
*The answer will be black people in the South, unfortunately, proving that the presence of such a population is incompatible with a unified and modernising state. On the left, I expect Jewish capitalists to be blamed for profiting from division.
** Nope. Though informal dominions a la Argentina aren't out of the question.