[Yossarian_Lives]

I think people forget that the EU exists somewhere between Federal-style government (the US for example) and pure international organisations (The UN, etc). You can look up where its sole and shared competences lie in articles 3 and 4 of the treaty that established it, but it's not a long list and mostly concerns the operation of the common market (the free movement of goods, services and people) and a grab bag of smaller roles.

The tension inherent in that set-up is between the individual powers of sovereign nations and the collective policy of the group. In this instance, there's no doubt that Sweden and the UK are helping the US in vetoing, but there's a parallel concern that the EU does not have competence to negotiate on this, and I imagine a strong desire to prevent mission creep.

As to the broader question of ungovernability - I'd argue that the really interesting question is whether it is possible to maintain a firewall between economic policy and everything else, which is what arguably distinguishes the EU from other forms of weak federalism. Even before the Euro crisis there were edge cases where economic jurisdiction bled into, for example, social issues (the ECJ ended up having to effectively rule on Irish abortion law under the free movement of services). Now it's even worse. Political parties in Greece and Ireland, for instance, have been co-opted into austerity policy by having the gun of exiting the Euro held to their heads. At that point the questions of the EU's democratic deficit and the sovereignty of its smaller members becomes more pressing. At some point, I suspect, the EU membership (Euro members especially) will find itself forced to pick between actual federalism and supra-nationalism.