With the Greek government facing imminent bankruptcy, there are fears the crisis could topple other heavily indebted economies and threaten the stability of the euro itself.
The summit was meant to be a low-key affair, an opportunity for the new EU President Herman van Rompuy to chart a postcrisis course for the bloc's underperforming economy.
The summit will take place in an elegant historic library building set amid a stretch of parkland in Brussels' euro-quarter. The unusual setting, van Rompuy says in his letter of invitation, is intended to stimulate "substantial thinking" among EU leaders on the future of their economies.
But what has come to be known in Brussels as the "Greek Tragedy" has wrought havoc on those carefully laid plans. The initial EU strategy of keeping a low profile -- in the hope the Greek government's promises of fiscal reform mollify the international money markets -- has not worked.
Addressing the European Parliament in Strasbourg on February 9, the EU's outgoing finance commissioner, Joaquin Almunia, acknowledged the EU must step in to respond to the crisis.
"The difficult situation in Greece is a matter of common concern for the euro area and for the EU as a whole as large and persistent external and domestic imbalances threaten the macro-financial stability of the country, with a serious risk of spillovers into other parts of the euro area," Almunia said.
Public sector debt in Greece -- as in Portugal -- now exceeds its annual economic output (GDP). Spain is not far away from emulating that statistic.
All three countries must pay off lenders tens of billions of euros this year. And this is becoming increasingly more difficult due to rising interest rates on new loans.
Risk To The Euro
Meanwhile, all three governments run annual deficits exceeding 10 percent of their GDP, meaning they are struggling to make ends meet. Greece has already been hit by a number of strikes by public sector employees -- among them tax collectors -- which undermine the government's willingness to cut costs by embarking on an austerity program.
Devaluation -- a standard remedy in such predicaments -- is not available to any of the EU's Mediterranean economies, which all are members of the EU's single currency, the euro.
The great risk is that a Greek default -- a public admission of an inability to pay back international lenders -- could develop into a run on other indebted economies, and eventually the euro.
Greece is a relatively small country and a bailout would not cost the EU too much. But paying off the debts of profligate southern governments is deeply unpopular among German taxpayers who would have to foot most of the bill.
German leaders have this week sent conflicting signals on whether a bailout could be in the offing.
Markets and experts alike believe the stakes for the EU are too high to refuse to step in and help out Greece, and possibly others, too.
Cinzia Alcidi, a research fellow at the Center For European Policy Studies in Brussels, told RFE/RL that EU leaders must show solidarity in the face of the crisis.
"It is necessary to provide the market and the public with a clear signal. And the signal that now is needed is that the EU -- generally speaking -- will not let Greece [collapse]," Alcidi said.
Bailout ... With Strings
One or more Mediterranean defaults could gravely undermine the euro and possibly lead to the break-up of the eurozone. Its rules do not provide for the exit of individual member states.
The collapse of the euro, in turn, would mean a drastic reversal for the EU. The euro was introduced on the tacit assumption that economic integration will lead to greater political integration among the member states.
While this assumption may have been a little optimistic, it appears unlikely there can be any further political integration if economic integration fails.
A successful southern rescue package, on the other hand, could speed up integration on all fronts.
Such a bailout would likely come with strings attached, as the benefactors would want to have control over how their money is spent -- at the very least, some say, over Greece's fiscal policy.
This could, in turn, feed into the wider EU debate on future economic governance, the original focal point of the summit. The European Commission, the EU's executive arm, has drawn up an "Agenda 2020" for the bloc arguing for greater coordination of economic policies among member states.
A joint session of the German and French governments last week also called for greater economic integration in the EU.
At the very least, the entire rationale of the EU's massive redistribution programs of funds from richer to poorer countries is now in question. The traditionally poorer Mediterranean countries have been the greatest beneficiaries of the bloc's "cohesion" funds, netting tens of billions of euros of aid money in recent decades.
Alcidi says this is something that is likely to give the EU pause: "We have experience of about 10 years of growth in the European Union, but not many countries behaved in the right way [throughout that time]. It was actually a period in which many imbalances were built [up]."
Alcidi says it is going to take years for the EU to put this new crisis fully behind it.