But it was hard not to feel real foreboding. Without a quick new deal with the creditors, Greek banks could collapse within days, introducing the country to a whole new level of economic misery. Pride and dignity would swiftly vanish, along with jobs and savings.
Mr Tsipras has said he can get a better deal from Europe. But, if he really believes that, he is seriously misreading EU politics. In reality, Greece's creditors are likely to take a very hard line. They are angry and fed up. More important, many also believe the long-term survival of the single currency depends on making it clear that countries must live by common rules, balance their budgets and pay their debts. If Greece needs to be punished to make that point, so be it.
The tragedy is that the Greek government and its creditors are both misreading their own interests. The Greeks still insist they want to stay inside the euro zone - despite the mounting evidence that it has been a disaster for their economy. The euro zone leaders feel they must be tough with Greece, to discourage other potential rule-breakers.
In reality, Greece and the rest of the euro zone should treat the Greek vote as an opportunity to rethink the malfunctioning euro project. They can find a common interest in making it as painless as possible for Greece to leave the euro - both to lessen the suffering of ordinary Greeks and to establish a model that other countries might be able to follow in the future. For Greece is not the only country struggling to cope with a currency union. This crisis could be a chance to show there are ways out of the euro that could benefit all sides - those that leave the currency union and those that stay.
But for the moment, all that euro zone leaders can see are the dangers of making any moves that appear to "reward" Mr Tsipras. They know there are many heavily-indebted countries in Europe and do not want to encourage the idea that countries can avoid the hard work of getting their national finances in order, in the hope that one day, a debt write-off might come to their rescue. Greece's national debt as a share of its economy is 178 per cent - the largest in the EU. But Italy's debt-to-output ratio is more than 130 per cent. Even France is closing in on 100 per cent, the figure that Greece was at when the markets first took fright in 2009.
There is a similar fear of the political consequences of allowing an anti-austerity party to triumph in Greece. Ireland, Italy, Portugal and Spain have all made painful cuts in an effort to restore their public finances. Their governments have Syriza-style, populist parties breathing down their necks. The last thing they want is for Syriza to be seen to succeed. Indeed, the grim truth is they have a vested interest in seeing Greece suffer - as a warning to their own voters not to take the route of left-wing populism.
In other EU countries, such as Finland, Germany and the Netherlands, it is right-wingers - who opposed the original bailouts for Greece and warned the money would never be repaid - that stand to gain if Syriza is seen to triumph. Here, too, the political incentives all point towards European leaders taking a hard line.
To these factors must be added sheer irritation. Finance minister Yanis Varoufakis, who compared Greece's creditors to terrorists, has resigned. But even Mr Tsipras accused the creditors of being conservative extremists, blackmailing Greece. Just as Greeks feel humiliated to be told they are deadbeats and debtors, so the Germans feel enraged to lend Greece money - only to be called Nazis in the Greek media.
The danger, however, is that anger and a fear of setting a bad example is leading EU nations to take too narrow a view of the consequences of Greek failure. Maybe the EU is right to believe financial contagion from a Grexit can be contained. But the political costs would be very high. A Greece that slips into economic chaos could easily turn into a failed state within the EU. That, in turn, would further discredit the European project - at a time when it is under pressure from all sides.
Instead of punishing Greece, the EU should do its level best to make sure it can leave the euro, but stay inside the EU with a minimum of pain. If that means giving Greece debt relief as part of the exit package, so be it. Debt relief, in return for Grexit, could make political as well as economic sense.
Even so, restoring the drachma in Greece without provoking an even more intense economic crisis will be hard. But, if it could be done, the EU may finally have a model for liberating other European nations from a malfunctioning euro.
THE FINANCIAL TIMES
