It would start with the recognition that Greece is insolvent. It can’t pay the money it owes. One or two or maybe three other countries also may be insolvent. And the existence of solvency problems in some states is creating liquidity problems for other larger states. So there’s some insolvency, and even though the insolvency is concentrated in a relatively small number of small states it’s a problem for a much broader set of European people. At the same time, if you look at the total amount of sovereign debt in Europe and compare it to the Eurozone’s total fiscal capacity, the debt is very manageable. The Eurozone as a whole is a very solvent, creditworthy entity. So in principle you could consolidate all that outstanding European debt into a single Eurozone-wide debt financed by a modest European Solidarity VAT Surcharge. Then you’d have to severely curtail (if not eliminate) the EU member states’ ability to engage in deficit spending, limiting them to some kind of authority to borrow from a central European entity. The EU itself would become a debt-issuing, taxing entity like a real country.
Yglesias comparison of the current European Union and the US under the Articles of Confederation is flawed but not without merit.