"If they fail to reassure bond investors, all of the nightmare scenarios come into play," says Robert Shapiro, a former U.S. undersecretary of commerce in the Clinton administration.
The biggest danger is a fast-spreading crisis known in financial circles as contagion — a term borrowed from medicine and familiar to anyone who has watched a disaster movie about killer viruses on the loose.
"It's like a disease that spreads on contact," says Mark Blythe, professor of international political economy at Brown University.
The bond market, where banks, traders and governments cross paths, provides the setting. If Greece dropped the euro, traders would become more suspicious of Spain, Portugal and Italy and sell those countries' government bonds, pushing their prices down and driving their interest rates up.
Higher borrowing costs squeeze those countries' budgets and push them deeper into debt. Plunging bond prices also would imperil Europe's troubled banks. The banks are big holders of government bonds, which they bought when the bonds were considered safe.
At this point, the risk would be high for a run on banks throughout Europe. People would worry that the banks might fail and would rush to withdraw what they could. Analysts and investors say that's the biggest fear.
People in Spain, for example, have already seen what's happened in Greece and have started pulling euros out of their accounts in fear the country will switch back to cheaper pesetas.
"People see their banks in trouble," Shapiro says.
In less frantic times, the government would come to the rescue with cash or take over the banks. Individual European countries insure bank deposits, so if one bank fails people can still get their money out. But all this is happening in the middle of a government debt crisis, and if the crisis gets worse, the Spanish or Italian government couldn't raise enough money in the bond markets to save the day.
"They can't afford to guarantee deposits or money market balances," Shapiro says. "They don't have the ability to borrow internationally from bond markets. Where are they going to get the funds?"
From here, the crisis could get much worse: Banks could fail, the surviving banks could stop lending to each other, and a credit freeze could shut down commerce in Europe as assuredly as a blizzard did last winter.
One way to stem the contagion would be to create so-called eurobonds — bonds backed by all 17 countries that use the euro. They could be sold to raise money to buy the bonds of troubled European governments. With the backing of 17 countries, including mighty Germany, eurobonds would have a yield far lower than the bonds of countries like Spain and Italy.
Germany, which has the strongest economy of the euro countries, has slowly warmed to the idea but wants weak governments to fix their finances first. "Germany's strength is not infinite," Chancellor Angela Merkel said Thursday.
Cash-strapped European governments should be able to turn to the International Monetary Fund for help, but the IMF's money comes from 188 member countries. Peter Tchir, who runs the TF Market Advisors hedge fund, says the U.S. and other countries may balk if the IMF asks for help supporting Europe.
He worries that the IMF may take a loss on the roughly $28 billion it has already loaned to Greece.
"People are happy to put money in if they think they won't lose it," Tchir says. "In this case, the IMF loses money, then everybody gets scared."
A full-blown crisis would cross the Atlantic through the dense web of contracts, loans and other financial transactions that tie European banks to those in the U.S., experts say.
Blythe, the professor at Brown, believes credit default swaps, the complex financial instruments made infamous by the 2008 financial crisis, would provide the path.
Banks created the swaps to sell as insurance for loans. After lending money to a business or government, investors can turn to a bank and take out protection on the amount they lent. If the borrower runs into trouble and can't pay — say, the government of Spain defaults — the banks that sold the insurance cover the loss.