People needlessly connect the EUR's fate to the fate of the European Union as a whole. It's just a currency.

The EU ought to be capable of reverting mistakes - THAT is critical for its long-term success and survival.

The EUR in its current shape was a mistake, and critics knew it back in the mid-90's. The economies are too different. Portugal and Greece did not belong into the common currency, and it would have been wise to set up a common currency (if at all) as a non-EU project. Maybe Germany should have stayed out of it, too. Germany, Northern Italy, Paris department and some other regions are the industrial centres of Europe and can be in a common currency with the less industrialised regions only with great adverse side-effects.

Actually, Italy and Germany would need two different currency zones each since even inside these countries labour mobility proved to be unable to balance the strains.
(In a simple theory monetary union theory moving labour solves a lots of common currency problems between dissimilar regions, but in practice many unproductive people stay behind and transfers from North Italy to South Italy or West Germany to East Germany are still necessary).