The United States is unlikely to break up. The Russian "professor" that they reference in the article seems to know less about the United States than the people who made the "United States of Canada/Jesusland" maps which were meant to be humorous. We are too mobile a society. Many of us have friends and family all across the country. I mean, you wouldn't want to cross a border to get to a relative's house. Nor would you want to have to deal with tariffs/importation on something you got from Amazon. If anything, the world wants less of that as evidenced by the European Union. Now, the US might become more localized and that would suit some, but we aren't going to see a dramatic breakup.
And what people forget is that, through all the nonsense that's gone on in the past decade, we aren't actually that different. We have a common culture, even if that culture is a result of many cultures. It binds us together even through the heated arguments of the recent past/present.
Catastrophe is unlikely as well for a few reasons. First, it's hard to replace the US government which makes it hard to implement any sort of unchecked policy. To replace the President takes 4 years; to replace the legislative branch takes 6 - and it can't be done on a whim, it has to be 6 years of people deciding to go the same way. In other governments, you can completely switch the government in a week. Second, there are more checks and balances. The executive isn't a prime minister, but rather separate from the legislature. And we have a constitution that grants limited powers and yes, to this day still provides a good check on authority despite what has happened in the recent past. Third, US politics are local politics. Senators and especially Representatives aren't easily replaced because they form roots in their communities. Even beyond that, you can't appeal to fringe groups to get elected. While 1% of the country might think that a fascist or a stalinist would be good to have in government, they get no representation because they aren't able to carry a district. In other countries, representation is usually done on the basis of how much of the national vote you get which means that radical elements have a much greater say in those governments.
Now, some of what I've mentioned above can come off as bad things - they certainly mean that it's hard to implement good, new policies. But that also means that it's hard to implement bad, new policies.
Plus, for all the crap that I'll give the US government, they are genuinely responsive to big things. I mean, unemployment is around 10% right now. In many highly developed places (like Europe), that's not even bad. And everyone on television is calling this the worst crisis of our time. Where I grew up, unemployment was, during good times, about 20%. Now, the US doesn't have the social services that make unemployment more livable so it's very harsh on those who are unemployed, but we've seen the government take steps to make sure that things, generally speaking, run smoothly. I mean, Argentina a little while back had a huge crisis that really wiped out the middle class - robbing them of the vast majority of their money (cash money). While one might not like some of the steps that the US government has taken, it has meant that no one's bank account has been lost (at the very least).
And Americans aren't radicals. I mean, I have friends who call themselves radical, but what they mean by that is that they have a CSA (community shared agriculture) and would like European-style socialism. Oh, and maybe taking a year off somewhere to work on a hippy farm. No guns, no violence, no death to people that don't think like them. No looting, no riots. . . We sure as hell yell about things and have strong opinions (like the Professor Gates incident in Cambridge, MA), but has there been mass violence in response or whatnot? No, life has gone on as normal.
Even when one looks at immigration, the US is one of the most immigrant friendly countries. That might be hard to believe given some of the rhetoric, but we're one of the few countries that still has "born on a rock, citizen of that rock". Even beyond that, what's our anti-immigrant policies? The biggest seems to be the national language debate which, while possibly symbolically important, wouldn't have a practical impact. I mean, anywhere that currently provides foreign language assistance would continue to. Laws are already written in English. English is the lingua franca. And yes, there is a dislike of "illegal" or "undocumented" immigration (depending on the side of the debate you come from) and there have been (in some places) harsh measures taken. But the attitude toward legal immigration is much better than in many places in Europe. France just a few years back had huge riots over this issue with wonderful flaming cars and all. Heck, the right-wing position in this country tends to be "well, smart people are always good to have coming in and the dumb ones are taking jobs no one wants anyway."
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There are simply too many nice practicalities to staying together (like currency, ease of travel and commerce, etc.) and too few radical elements. And the US has a great history of absorbing immigrants and facing the problems that have befell it. I mean, we got through a civil war, two world wars, and the cold war. While we might have problems now, they aren't of the same magnitude. Yes, we need to face the challenges of today. However, the challenges of today aren't so bad when you compare them to sending your kids to Vietnam - or being sent there yourself. A touch job market != being plopped down in south asia with an automatic weapon expecting to survive a few weeks.