Its economics, clearly, has run ahead of its politics, but the financial crisis has highlighted another existential threat to the EU - its legitimacy deficit.
While member states and the media debate the legal questions and the technicalities over the latest integration plan, and leaders engage in nationalistic chest beating over sovereignty, the root of public protests, parliamentary revolts - even the debt crisis itself - could be the EU's failure to offer its citizens real participation.
In November, George Papandreou stunned the eurozone by saying that he would take a hard-won eurozone rescue plan back to the people that elected him, and give them a choice over whether to accept it.
The package, which included more bailout money and debt relief, in exchange for deep public spending cuts, promised a credible way out of Greece's troubles, but at the cost of real economic pain for the Greek people.
Calling for a referendum was a calculated political gamble, aimed at trying to ease the sense in Greece that the people were being force-fed a very unpleasant medicine and give the electorate a semblance of democracy.
The markets panicked, Papandreou was summoned to Cannes, where Angela Merkel and Nicolas Sarkozy were meeting ahead of the G20 summit, and the referendum, along with the Greek prime minister, quietly disappeared.
Since the beginning of the crisis there has been a sense that he - or she - who pays the piper calls the tune, with a widespread assumption amongst market commentators that since Germany held the purse strings it had free rein to reinvent Europe with only the broadly acquiescent France as its opposition.
Of course, Germany itself is financed on the international capital markets, as are most of the rest of the eurozone's economies, and the past year has been a constant effort to try to keep yields on peripheral bonds below unsustainable levels.
As temporary fix after temporary fix failed to satiate the markets' desire for clarity over whether the single currency would survive, the tenor of conversations around the long-term vision of the European "project" - a term still used largely without irony by Brussels observers - changed.
It is difficult to pinpoint when it started, but over the summer a clear momentum developed, beginning in the markets, driving Europe towards a point that it once aspired to, but barely thought it would get to - the fiscal union originally envisioned by the euro's architects.
Fiscal integration requires member states to relax their sovereignty over their economic management. If confirmed, it is a step change in intra-European relations, well beyond the watered-down attempts at creating a unified constitution for the EU - the Lisbon Treaty - in 2009.
Achilles Skordas, a former adviser to the Greek government on European legal issues and a constitutional expert at the University of Bristol, told the Huffington Post UK that the Lisbon process essentially failed because there was no practical need for it at that moment.
"There was just a design, a project by some of the elite, but that was rejected because nobody saw any reason why power should be ceded to a higher level without any practical necessity at that moment," Skordas said.
"Now that necessity has come, the real transfer of power, the essence of the union, the economic governance, is becoming a reality."
Europe is not, as the more rabid eurosceptics in the UK, Finland and the Netherlands might have it, an aggressive, power-grabbing dictatorship run by unelected elites.
It is more likely a benign technocracy run by a combination of ideologues, bureaucrats and, yes, unelected elites. In times of crisis, national governments have an irritating tendency to stand in the way of reforms that benefit the greater good - as demonstrated in Greece in November, and by Slovakia in October. The Slovak government had the integrity to tie its vote on whether or not to scale up the bailout fund - the European Financial Stability Facility (EFSF) - and give it greater powers to a vote of confidence. Both failed.
To a large extent, the two have balanced each other quite well, resulting in a slow, steady and largely conflict-free shuffle towards greater cooperation. The sovereign debt crisis ended that happy balance.
Papandreou's bold gambit highlighted a growing divide between the need and democratic right of self-determination within and by EU member states, and the technical necessities of building the supra-national structures needed to make the crisis response meaningful and effective.
It seems as though the technocracy is winning.
The prime minister was replaced by Lucas Papademos, an unelected technocrat. In Italy, the colourful playboy politician Silvio Berlusconi gave way to the relatively staid and dependable Mario Monti - also unelected.
The cut and thrust and uncertainty of democratic transitions would have sent yields skyrocketing, so they were foregone, raising the question: can the demands of the stability of the super-state be reconciled with the individuals' franchise?
"I believe, as many other scholars believe, that it is extremely difficult to replicate the democratic structures beyond the nation state," Skordas said. "We have evidence of that in the developments of the last couple of months."
Richard Youngs, the director of the Spanish think tank Fride, told the Huffington Post UK that while it is easy to engage in hyperbole around the erosion of democracy by the demands of the financial markets, "There's certainly a danger" that structures are being undermined.
"This has become a common argument now, that markets are somehow hollowing out the substance of democracy," Youngs said. "One could say that there's a slight irony, in that this isn't a new discovery for many developing countries, it's exactly the problem that they were complaining about for several decades in respect to IMF structural adjustment programmes that were imposed on them by European governments."
Youngs said that the root of the problem has been the inability, or unwillingness, of governments to properly communicate to their electorates how the European contract works.
"The nature of the political debate in Europe hasn't been positive or sophisticated enough to realise the kind of trade-offs that are needed to maintain the euro," he said.
"It isn't really a crisis of democracy per se, but it's that public opinion under democratic states is wanting quite incompatible things. 80% of Greeks say they want to stay in the euro, but 80% of Greeks also say they don't want the reforms that are necessary to abide by the rules of the euro. There's an incompatibility of choices that are being expressed by democratic populations."
The perception in Spain - which has seen enormous benefits from its membership of the EU - is very much that the deal is all upside, Youngs said.
"The wider set of rules that govern the political economy of the euro were never really explained, so it's seemed to be purely a positive benefit, without the more rigorous rules that were needed to stay firmly in the euro being fully explained to the population in general, or I think fully understood by the political elite in the country," he added.
This is why - as in Greece, the UK, even in Germany - public support for the European "project" seems to wane at the precise moment it needs to be strongest.
A lack of a sense of agency amongst European citizens means that, as major decisions are taken in a remote centre of power, their national leaders are vulnerable to domestic pressure to "protect our interests" along narrow lines of debate, with the blunt tool of referendum the only recourse to participation.
The only way to fix this and save the project, some experts say, could be to create a real democratic mechanism within Europe.
"The European integration process has for the past 50 years on output legitimacy - on the fact that it produced good things for people. It was alway producing those, and as long as it kept producing more, it felt sure that people would think it was a good thing and would underwrite it silently," Jan Techau, the European director of the Carnegie Endowment for International Peace.
"But political systems cannot work on output legitimacy alone. They have to have input legitimacy, which is a democratic mandate. That is the way they allow the citizen in the street participate in the decisions they are making."
The participatory mechanisms of the union have not developed in step with the political and economic integration of the EU. When the French and Dutch electorates voted against the adoption of an EU constitution under the Lisbon Treaty, this should have been a warning sign that the two were now strides apart, according to Techau.
"We have now gone over that point, and we have gone way into territory that is uncharted, and where the popular mandate is not enough anymore to pull all these [integration steps] off," he said.
"If the European Union wants to go ahead with the integration steps that they agreed upon at the last summit, they have to develop a system on the other side of the spectrum that allows for popular participation. You have to come up with some idea about how you can pull people into the political process. That means elections."
This does not mean repeating the current European elections, which are fought on domestic terms in the 27 member states, between domestic parties. The system is not widely seen as representative, with parties otherwise excluded from mainstream politics in their home nations often scoring victories after campaigning on single issues. This failure is highlighted by the relative absurdity of staunchly eurosceptic politicians taking seats in the centre of European power.
Techau thinks that a "real European competition of ideas" is needed, where individuals vote on a continental level, rather than being represented through an aggregation of national politics.
"But the direct result of that is the formation of a European demos, a European voting people, an electorate, and that is one of the key thresholds for forming a state. And now we're getting into really dangerous territory," he said.
It may sound like "science fiction" in the current political landscape, he added, but it is essential to give the economic structures a scaffold of legitimacy.
"There is an ultimate need for legitimacy in the current system. But the legitimacy cannot be created without a drastic step, that is also a step towards statehood," he said. "That's the huge dilemma, and the entire legitimacy question of the European Union.
The choice could be to take that drastic step, or to fall apart. The history of integration has been one of moving forward in terms defined by the grand vision of the European project. Never has such a step been taken against a backdrop of a real, existential threat to the union, and with such an impetus from an external actor - in this case, the international financial markets.
"We reach a point in the European project where it is not a project which is decided in mutual love, but in mutual angst," Skordas said. "This is something that can be interpreted as consensus, but it's something more dark than an optimistic project from the future. It's the product of a very strong necessity of the moment, and it's the product of angst."