Having dismissed the decision of the Greek government to hold a referendum this Sunday on the country's economic future as a reckless gamble, European leaders hope that, even at this late stage, the people of Greece will pull back from the brink of disaster, sparing the rest of Europe a broader crisis.
But there is also a growing realisation in European capitals that, regardless of how this Greek showdown ends, the problem won't go away.
Even if the Greeks decide on Sunday to accept austerity measures in order to retain the euro as their currency, a default on its debts to the International Monetary Fund (IMF) will present new problems, including the potential to set off a cascade of cross-default clauses.
It is also a thorny reminder that regardless of all the institutions which the European Union has created, there is still no substitute for good governance at the national level.
The event will also have deep implications for the IMF itself. The institution, which has been dominated by Europeans since its creation at the end of World War II, stands accused of spending far too much on a relatively wealthy European country, and far too little on its truly poor nations.
That won't be forgotten when Ms Christine Lagarde, its current boss, seeks re-election next year; the Greek episode may cost the Europeans their commanding seat on one of the world's most influential bodies.
Meanwhile, ordinary Greeks are guaranteed years, if not decades, of misery. If they vote "no" in Sunday's referendum, their country will be ejected from the euro zone within days.
True, no legal procedure to evict a European nation from the single currency area exists, but events have their own way of creating facts: Once Greek banks melt down as they surely will, and once the Greek government runs out of cash to pay its civil servants and pensioners, the country will have to issue a new currency.
So, it's not so much that Greece will be evicted, but more that it will eject itself out of the euro; threats by Greek ministers to "sue" the EU if they are thrown out of the euro zone are just typical of the absurd, surreal attitudes now prevailing in Athens.
Yet even if the Greeks vote to accept the austerity package currently on offer, it is difficult to see how this would resolve matters. Having campaigned against accepting the bailout deal, the Tsipras government will have neither the credibility nor a political stake in implementing the austerity.
Chances are high that Prime Minister Alexis Tsipras will resign and call new elections, something which will only plunge the country into bigger mayhem.
And it's a certainty that, even if elections are avoided and even if the bailout package is accepted, Greece will come back with the begging bowl in a few months from now, when it again runs out of cash because it had not implemented any of the obligations it has undertaken.
European leaders have every reason to be furious with a Greek government which has persistently distorted the nature of its problems. It's simply not true that Greece is being abandoned by its European partners; the Greeks have benefited from the biggest bailout package ever put together, worth €240 billion (S$360 billion).
Nor is it true that the fundamental problem is Greece's huge debt. The Greeks currently spend less on repaying their debts than almost any other European nation; the Greek government is merely using the debt question as a decoy to justify its refusal to adjust current national budgets in order to avoid falling into the same debt trap in the future. This is a battle about Europe's future stability, one which the Greeks want to cast as a fight about the past.
And it's simply not true, as Mr Tsipras claims, that by insisting on continued economic austerity, European leaders are "ignoring" the "democratic choice" of Greek voters. For, quite apart from the fact that it is never up to the debtor to decide unilaterally how to repay creditors, the EU bent over backwards to make compromises. Yet all were ignored by Mr Tsipras, who gambled that the Europeans would ultimately blink.
It was, as EU Commission President Jean-Claude Juncker aptly put it, a "game of liar's poker", one "not worthy of the great Greek nation".
Despite dire warnings that the Greek crisis threatens to unravel the European Union project, in some ways it may reinforce it. No other continent has spent so much time and money on protecting a country as Europe has done.
And even those Greeks who would vote "no" to austerity on Sunday will do so while believing in their place in Europe. The Greek problem is not necessarily a harbinger of things to come, but an exception, proof of what happens to a nation unwilling to keep up with the governance standards of its partners.
