I don't know that we'll see the collapse of the Union, but I can certainly imagine a break up of the euro, with coutries reverting to national currencies. Of course, this would prevent further unification, but I don't see the current political institutions really disintegrating. More just that they remain fairly static.
As far as social welfare and entitlements, I don't think the issues with the peripheral euro states are a result of them per se. Instead, the budgetary situation in these countries is dire because they have bloated government workers, their underlying economies are weak, and yet they want to maintain a generous level of social welfare. Something like 25% of all greek workers work for the government. That's just not sustainable. Contrast that with say Germany. They have a much stronger underlying economy, driven by a productive export sector. They can better afford the social spending they are doing. Now, why exactly it is that Germany is in one position and the PIGS (Portugal, Ireland, Greece, Spain) is a question that has no satisfactory answer. I'd guess because it has no single answer.