The choice is destruction slowly or quickly. The slow path is for the EU to let Greece return to the Drachma, devalue, and let their economy recover by low-cost exports. The problem is that Spain and Portugal are in almost as bad shape, and the temptation to join Greece will be high, and Italy and Ireland (almost as bad as Spain and Portugal) would be next. The dream of the European super state would collapse over the course of 2 or 3 years.
Adoption of the euro, by removing the threat of currency fluctuations, encouraged yield-hungry investors to bid up Greek bonds. Leverage allowed Greece to run big current account deficits, despite low productivity growth. The result, once the credit bubble burst, is today’s crisis. There is no easy European fix.
Greece has two main options to restore competitiveness and narrow its current-account deficit: Withdraw from the euro and devalue, or win large and ongoing transfers from European states with surpluses like Germany.
Fast is where the healthy EU economies (*cough* Germany *cough*) essentially subsidize Greece's spendthrift ways. Unsurprisingly, this will massively unpopular in Germany, where the population (correctly) believe that they're already subsidizing much of Europe. To mollify German public opinion, the European Central Bank would have to put Greece on some pretty stringent austerity measures; these (unsurprisingly) will be wildly unpopular in Greece, and will accelerate the exit strategy. Nothing like a little resentment to fire the blood of independence.
All in all, the problem is that it's far too easy to free ride in the Eurozone, at least if you're a smaller economy. And maybe even a big economy (*cough* Italy *cough*). Closing this will take more strong central control than it's likely that most of the European governments are willing to cede to the EU - it's one thing to get some free EU loot to kiss up to Brussels, it's quite a different thing to give budgetary authority to them.
Stick a fork in it. The EU core (FIGS - France, Italy, Germany, and Spain) along with BENELUX will keep going for a while, but expect to see the Eurozone shed some peripheral nations over the next 18 months. After the third one leave (say, after 4 or 5 years), expect to see serious action in Spain and Italy. After than, what's really the point, other than the French cat shacking up with the German dog.
And the worst of it for the EU Parliament? Nobody really will care.