Having lived in Germany when the Euro was adopted, I am very skeptical that the debt crisis on the fringes of the EU will cause the whole union to founder or the Euro to disappear. Too many politicians and too many parties have too much political capital invested in these structures. It would take a new generation of politicians, and possibly a new set of political parties, to muster the political will to dissolve the EU.
It is more likely that some of the fringe countries will get expelled from the Euro Zone to save the currency. Even this step would require a major policy changes, but it may be more feasible than dealing with the internal discontent in Germany, Austria, and other Euro Zone countries.
Now let us take a look at the size of the credit problems in Europe. The main worry is that banks in the more robust countries have made loans to individuals, companies, and governments in the fringe countries. Those loans could become worthless if these countries default.
According to this article, the total exposure of banks in the Euro Zone to Spain, Portugal, Ireland, and Greece adds up to about $1.6 trillion. Most of that is concentrated in Germany and France. This is about the same as the outstanding subprime mortgages at the peak of the bubble in 2006 (13% of about $10 trillion according to Bernanke).
The current US GDP is about $15 trillion. Again this is very comparable to the GDP of the European Union of about $16 trillion. The expected debt to GDP ratio for the US for 2010 is 94%. For the EU this number is expected to be around 80% for 2010.
In the extreme case that the EU would borrow $1.6 trillion to buy the entire fringe exposure from all European banks at face value, their debt to GDP ratio would jump to about 90%. That is a very uncomfortable number, but still significantly lower than the US ratio.
The point of this exercise is to show that the European debt problem is certainly large, but the EU is in a much stronger economic position than the US and would be able to bail out their banking system if that turns out to be necessary.
It is likely that the news out of Europe will cause some market turbulence. It is possible that some fringe countries will get kicked out of the Euro Zone, but it seems unlikely that the Euro or the EU will founder on this problem unless or until France and Germany elect much more EU averse governments.