I think the crux of the problem is that a fiat currency doesn't just attempt to capture the current resources, debts, and means of production for a country (or group of countries, in this case). There is also the element of future resources, debts, and means of production. I suspect uncertainty in the future is the main cause for all the recent problems, in the Eurozone and elsewhere.
Consider the times we are living in. It is likely that we are reaching a point that humanity has never faced before and will never face again (at least, not humanity as we recognize it). I like to call it "stationary phase", after the same concept that occurs in growing populations of bacteria.
Essentially, human population growth is beginning to decelerate. Changes in infant mortality and life expectancy are leading to vast demographic shifts that will most likely be permanent. What does this have to do with a fiat currency and debt?
Consider why one would take on debt. If I can acquire resources at a fixed constant rate, then it makes no sense to take on debt instead of simply saving up over time. Debt only makes sense when the means of production, and therefore resources available, accelerate over time. I can borrow now, because even though I have to pay back more later, I will have more even than what I need to pay back at that time.
So what causes means of production to accelerate? Lots of factors to be sure: more raw materials to exploit, gains in efficiency, etc. A very large factor, however, is accelerating population growth. Even if materials available and efficiency remain constant, more workers means more production and an accelerating growth in workers means an acceleration in the means of production over time.
But that's all coming to and end in the near future. So, to compensate, we could accelerate the exploitation of raw materials. Unfortunately, one of the most important raw materials for human economy, oil, is also decelerating in its rate of exploitation.
That puts the entire onus of accelerating means of production on increases in efficiency. Consider it a call to arms for knowledge workers around the world. The only other alternative is to fundamentally change the way that economies work. If we cannot accelerate the means of production, then we cannot run economies based on debt.
What makes this whole situation all the more interesting is that if population growth stabilizes at some future point (i.e. zero real growth), then we may be very close to reaching the point where current means of production are sufficient to satisfy the needs of the existing population. Ultimately, the need for debt is based on the desire to borrow from the future so that we can do what is necessary to accelerate means of production, so that the means of production can catch up with accelerating population growth. If everything gradually comes to a halt simultaneously, then we may just reach a "stationary phase" where the most important goal for economies is to remain stable, as opposed to today where the most important goal is exponential growth.
That, unfortunately, is the optimistic view. If things don't quite mesh up, expect the next century or so to be rather messy...