(Fortune) -- Athens is abuzz with a rumor: Greece might leave the euro zone and adopt a new currency -- a Greek euro, so to speak, something of a cross between a drachma and a euro to be used only internally. Some hungry economists have jokingly given the new money a nickname: the "Gyro."
If only the solution to Greece's problems could be rolled up as neatly as a gyro sandwich. A bailout from the European Union or its partner countries is growing increasingly unlikely -- German Chancellor Angela Merkel just put a kibosh on discussing the topic at the upcoming EU Summit. While the International Monetary Fund sits in the wings ready to swoop in, it is unlikely the EU would allow its aid, and stigma, to affect the other Euro nations.
As a member of a currency union, Greece is "stuck in a Euro-zone straightjacket," writes economist Desmond Lachman of the American Enterprise Institute. Its options to dispose of its debt are limited: a default is not politically viable, a restructuring is unworkable, and currency devaluation to make the mess go away -- a tactic Argentina used in 2001 -- is impossible. To remain in the EU, Greece must accept its rules in good times, and in bad.
If Greece thinks it's trapped in a bad marriage, it could choose to leave the eurozone, but that would be a shocking development, one that prime minister George Papandreou insists is not on the table.
Yet the country may have no choice -- Greece might even be asked to go. As the crisis deepens, Greece's "leaving the Euro area, though still a low probability scenario, can no longer be ruled out," says Uri Dadush, the director of Carnegie International Economics Program. "It's a painful route, but a lot less painful than others."
Greeks are starting to wonder what a euro-less future might look like. One possible roadmap: copying California's 2009 debt solution of issuing warrants later redeemable for dollars.
The proposal by London School of Economics' Charles Goodhart and Oxford Said Business School's Dimitrios Tsomocos, would introduce a new way to pay debts inside Greece (or any of the other ailing "Club Med" countries -- Spain, Portugal, and possibly Italy), while leaving the euro in place for international transactions.
Countries would print scrip that would act and look like a new currency domestically but not be legal tender overseas. There would be an exchange rate that would allow citizens to convert scrip to euros when necessary, but also allow the countries to devalue their economies while not affecting the euro's strength in other eurozone countries.
Other economists like Michael Arghyrou of the Cardill Business School and John Tsoukalas, a lecturer at the Nottingham School of Economics, have proposed a grander version of this idea, where a two-euro European Union would be formed. One euro will serve the union's weaker economies like Greece and Portugal, and another would circulate in the rest. In their plan, both currencies would be overseen by the European Central Bank. "We can't deny that at the moment in Europe we have a two-speed European economy," explains Arghyrou. "This is not such a big mental leap."
Arghyrou believes the plan would calm international markets because it would provide a credible outcome to the guessing game that's happening now. But the political debate likely to follow such an arrangement will be anything but serene. Whatever countries get the cheaper Euro aren't much going to like the stigma of using the weaker currency, Club Med or not.
Countries assigned to a junior currency might protest, but can their sovereign pride get in the way of hard facts? "The euro as it is now is not sustainable," says Arghyrou. "We'll be talking about 27 currencies ten years from now, not two, if the present trend continues."
"The euro was set up with a handicap," says Italian economist Mario Nuti. "It's a currency without a federal state, without a fiscal authority and without a budget." In the end, the fact that the EU is a currency union without a political foundation may turn out to be its death knell.
How this plays out for the European Union rests in Greece's hands. The task ahead is Herculean: The government must cut budget expenses by about 25%. "That's a heavy lift. If they do, it would be a miracle," says Charles Calomiris of Columbia University's business school. "But then again they said the same thing about the 2004 Olympics. No one thought Greece would pull it off, but it did." One could say it takes a Greek to figure out how to make and eat a gyro, all without spilling a drop.