With its language of budget cuts and bailouts, the sovereign debt crisis that is now engulfing Europe’s economies appears to be a financial crisis. But it is also, and perhaps foremost, a grave political crisis about the postwar European project itself: the European Union. And just as a Greek default will echo globally, the EU’s political crisis carries resonance beyond Europe’s own unhappy shores.

The travails of the eurozone have revealed a fundamental, and for too many politicians, still inadmissible, flaw in the European Union. Europe’s populations have been consulted too rarely in this project. And people feel little responsibility for decisions of which they are not part.

Greek voters are resisting the savage austerity cuts demanded by the IMF and other creditor countries – particularly Germany – to bring Greece‘s enormous debts under control. German voters are increasingly hostile to the bailouts, paid for by them and taxpayers in other creditor nations, to keep the Greek government solvent.

Further afield, citizens in both creditor and debtor countries, whether Finland or Ireland, the Netherlands or Spain, are turning against the obligations required of them by the crisis – to accept painful austerity, or to pay for others’ debts. Their hostility is understandable: few voters understand why policies imposed by distant institutions like the eurozone finance ministers, or the IMF, should be respected as their own.

The chickens are coming home to roost. Europe’s political elites are now paying the price for failing to ask Europe’s citizens what kind of European Union they wanted. Apart from Ireland, not a single EU government bothered to consult its own people on whether they agreed with the latest treaty, Lisbon, to give the EU’s institutions yet greater powers. The reason? Most did not trust their own populaces to accept the treaty, so they took the decision on their behalf. Many countries barely approved the Maastricht treaty, which, in 1992, launched the project of Economic and Monetary Union. Several allowed their citizens no say in the matter at all.

Some have proposed that the answer to the eurozone crisis is greater political union: that more centralised decision-making is necessary to harmonise financial policies, including borrowing and even taxation – for many, the heart of the sovereign rights of national governments. This may be the logical response of the policymaker, and it would, indeed, help remedy the imbalances that are now destabilising the euro, but it would be entirely wrong. For it is clear that when the going gets tough, as it is now, the EU’s decision-making institutions struggle for support among Europe’s peoples. This is a crisis of legitimacy that must be heeded.

One well-known senior EU official once told me that legitimacy of political institutions grows from the bottom up – people have to choose to give institutions authority. The trouble is that the EU’s structures have been designed from the top down, by politicians telling people that their carefully designed structures should be respected as legitimate, but almost never giving anyone a chance to say yes or no. This method of constructing Europe is the wrong way around, and it would be disastrous to repeat the mistake by imposing yet greater political union to save monetary union.

Europe is at a pivotal moment. Others observers, like the Economist, have outlined what needs to be done to solve Greece’s debt crisis, and this will be far from easy. But more challenging still will be resolving the political crisis, one of legitimacy, that Greece’s drama has uncomfortably revealed.

Europe’s political leaders have long paid lip-service to the EU’s “democratic deficit”. But this may no longer be enough.

Far right forces in the Netherlands, Finland, France and beyond are rising. These parties, like the True Finns and Geert Wilders’s Party for Freedom, are already exploiting popular anger at the euro’s turmoil, just as they have on immigration – another issue where more progressive forces have failed to make the positive case. Meanwhile, because the EU is their design, and their authority is at stake, Europe’s leaders will not be as quick to address the EU’s crisis of legitimacy.

This, then, is a dangerous moment, and not only for Greece’s economy, but for the political future of the continent.