In the U.S. there is ~$14 trillion in government debt. There exists tens of trillion more in private debt. But only $2 trillion exists in bonafide, actual, real honest-to-goodness dollars (I'm including in that count accounts at the federal reserve, not just paper money).
How is this system sustainable? How can any of this debt ever be repaid? Well, since everyone knows the government can print money, most people do not worry about the government being insolvent. A dollar T-Bill is as good as a dollar green bill, both are backed by the full faith and credit of the USG. If the government needs to, it can always print money to redeem mature treasury debt. Since no one worries about insolvency, most people would rather have treasury bills (or a deposit account or CD backed by TBills) because they pay interest. So the $14 trillion rolls over in perpetuity. In reality, $14 trillion is not really debt, since it is nonsensical to speak of debt that one owes oneself and can negate by printing paper. The $14 trillion is the money supply - T-Bills are just a dividend paying form of money.
However, the situation in Europe is much more sticky. Europe runs the same type of monetary system. There are tens of trillions in Euro denominated debt, but only $1.3 trillion in actual bonafide Euros. However - unlike with the dollar - the countries that created this debt do not have the power to create Euros. So as suddenly as markets lose confidence in the debt, it becomes impossible to roll over the debt and pay it off. There simply are not enough Euros in the world to pay off even a small amount of debt. Every single country in Europe would be insolvent if investors look down and lose confidence. Even Germany could not pay its debt if investors demanded redemption at maturity The European Union government could order the european central bank to print money to buy out the debt, but this creates all sorts of political conflict as it results in transferring real wealth from country A to country B.
So that's why Europe is stuck. It adopted a monetary system that works when the government controls the currency, and adopted it in a situation where governments cannot print money. No one in Europe has the brains or authority to actually refactor and re-architect the system, so they are just muddling around, following the path of least resistance and putting in stop-gap measures.
My own pet solution is on my blog: http://intellectual-detox.com/europes-crisis/ If anybody from the ECB reads Hacker News, I am available for hire as a consultant at the low, low fee of 1 ounce of gold an hour :-)