Republic is funny word. While I am skeptical of Sam Spade's economic collaspe, US turning into a dictatorship thing, mainly because I don't think an openly totalitarian or authoritarian system would work here, I have a hunch that the next century will not be good for anyone, whether it be China, Europe, or the US.
I think resource shortage, falling birthrates, and ethnic strife will hit everyone. Of these three, I actually think the US is best able to weather them. China has a demographic disaster, while Europe is less able to absorb the immigrants it is bringing in as the solution to its own. The US will suffer, but the fact is that is also isolated from where the giant humanitarian disasters are likely to be(Africa, Sub-Continent).
Weather is a mutable word. As the world heads for disaster in the 2020s, I fully expect the US to turn isolationist and xenophobic, probably with a soft-authoritarian de facto one party state. More Children of Men than V for Vendetta.
Oddly I actually came up with a time-line about this in my head that I never posted.
So. Will the 21st century be like the 20th century, the 5th century or the 14th century?
I think a bit like the 5th century. A lot of modern civilization is only possible because of cheap energy. All this talk of alternative energy, new drilling, etc. ignores a key fact, which is that we are on a long-term path of inflation. All alternative fuel types, whether electric or ethanol are still subject to this at the end of the day. How people adapt to that is going to be interesting.
Basically I see in Europe the anti-immigrant euro-skeptic right taking power, either through people like Wilders(not like Haider or Le Pen, they are not credible) or by co-option of the traditional right. This will lead to a cycle of increased polarization, efforts by an EU bureaucracy to crack down that feed anti-EU sentiment. i expect the EU to collapse by the 2030s.
The reason for this is simple. Freedom of trade, freedom of movement are only beneficial if the whole pie is growing. That largely stopped in the West a while ago, and the illusion of it has been kept up by currency inflation. When this myth falls, and it becomes clear that there is a shrinking finite pie, then the cries of the people at Goldman Sachs for efficiency and a flat world will be replaced by demands we keep people employed at our own car companies even if they are inefficient.
Despite the present fight over immigration, I expect the US to mostly avoid that problem, but the rise in gas prices will lead to a lot of political problems and a move towards isolationism. Self-sufficiency.
The really brutal thing will be China trying to grasp resources like oil that it needs cheap, but the sources of which will begin to dry up. Watch what China does in Central Asia. I fully expect them to be the target of Islamic extremism not the West as the US recedes into isolationism.
Ah this sounds science fictiony. Probably better on the other thread.