It's probably a little hyperbolic at this moment to consider the country fissuring this way, but considering the widespread corruption, election fraud, union bullying, and strident propaganda that has allowed certain urban areas to dictate the rest of the country's leadership, I don't think it's much of an exaggeration to state that the country already has broken up. This is not a President or an administration that has the slightest intention of healing anything; their strength is through hatred and divisiveness. And we have four more years of this to go before the same team ramrods Hillary through for eight more.
Which state(s) that would be that not only want to be independent but are also singularly strong in military sense, to ensure that they are left alone?
Note that if a state (say, TX) is strong enough to defend itself then it is also strong enough to annex the neighbor - which is the same problem, just seen from the other end.
I don't think it's much of an exaggeration to state that the country already has broken up
Politically - yes. But in terms of control, the country is as solid as ever. Perhaps it is even more cohesive, with expanded rights of the federal government and with reduced rights of states.
The real dissolution begins only after the central government loses power. That may happen for a number of reasons, but financial troubles are the likeliest cause. At some point the strongman in Washington will be unable to provide food to the millions of people who depend on the government. Within a week those millions will be very hungry and very unhappy, to put it mildly.
It will be China, most likely, who will pull the trigger. They will do that when they sufficiently divest their dollar reserves. The rest they will use as a pretext for claiming ownership of everything in the USA, at an opportune time, when the nuclear forces are defanged by the civil war, hunger, and by special ops teams.
Get real. Have you seen Hillary lately? She looks like she's aged 30 years in the last 4. She won't be fit for anything but a rocking chair and a drool cup in another four years.