To get a sense of how vulnerable the U.S. economy could be if the euro currency union cracks apart, start with the volume of U.S. exports to the euro zone — $153 billion in the first six months of the year. Add several hundred billion dollars in investments by U.S. banks in the euro zone and several trillion dollars’ worth of other financial contracts between the two economies.

As European leaders meet later this week to try to resolve their spreading debt crisis and prevent the breakup of the 17-nation euro zone, U.S. politicians, corporate leaders and financial analysts are watching anxiously for a breakthrough.

The alternative could be staggering for the U.S. economy. American banks and other companies could find themselves battling with any country that leaves the euro union and reinstates its own currency.

“The risk is likely paralysis,” said Michael Hood, a market strategist at J.P. Morgan Asset Management. “You won’t even know what people owe you.”

The summit this week is the latest in a long series of meetings convened to deal with problems that have expanded from concern about Greece’s high levels of government debt into a full-fledged threat to the euro union.

Although a solution has eluded them for two years, European officials insist that the worst-case outcome — an exit by one or more countries from the euro zone — will be avoided.

But a steady erosion of confidence in European leadership and the failure of previous crisis plans has made a once-taboo topic part of the mainstream discussion. Leaders now speak openly of the stakes, and German Chancellor Angela Merkel and French President Nicolas Sarkozy said Monday that they will push for wide-ranging changes in Europe’s basic treaties to help ensure that the currency union remains intact.

Analysts, meanwhile, are looking at different scenarios and sketching out the implications.

An exit by Greece alone could probably be stage-managed with help from the International Monetary Fund and the rest of the euro zone without much global fallout, according to a recent analysis by ING financial markets research chief Mark Cliffe.

Banks, companies and private investors have in a sense been preparing for that possibility for several months by pulling money out of the Greek banking system, liquidating investments and selling off Greek bonds at fire-sale prices. That has intensified Greece’s problems in the short term, but it also means that the world has less at risk in that country today than at the start of the crisis and could more easily cope if Greece left the euro zone.

Some analysts even advocate that Athens give up the euro as a way to help the country recover. Reintroducing the old currency, the drachma, would make Greek exports and investments cheaper and give the country control over monetary policy that is currently in the hands of the Germany-based European Central Bank.

According to data from the Bank for International Settlements in Switzerland, U.S. banks have less than $100 billion at risk in Greece, and only $4.7 billion in the government bond and bank investments that would be considered the most vulnerable to losses as a result of the crisis.

But Cliffe, Hood and others worry that a run of departures from the euro — starting perhaps with Greece and potentially continuing with Portugal, Italy and Spain — could have a catastrophic impact, leaving few parts of the global economy unaffected.

The euro zone would rapidly lose as much as 10 percent of its roughly $12 trillion in annual economic output, Cliffe estimated. The falloff in U.S. trade, a downturn in the financial sector and other impacts would almost certainly throw the United States back into recession — a risk that the Obama administration has highlighted by pressing European officials to be more aggressive in their crisis response.

“A continued slog [in Europe] would probably not show up as a big shock to U.S. growth,” said Jared Bernstein, a former administration adviser and a senior fellow at the Center on Budget and Policy Priorities. “But a real destabilization and breakup of the zone would have a significant negative impact.”

So far, that impact has been muted. Even as the euro crisis has intensified in recent weeks, U.S. growth has picked up. Officials at American multinational companies note that much of their manufacturing for sales in Europe is now done over there — not done in the United States for export. So while a European recession might hit corporate profits, the more acute effect would be at plants and on production lines in Europe. But U.S. trade with the euro area is substantial, and a deep downturn could hit U.S. companies hard.

The financial sector offers another channel of transmission for economic problems. According to the Bank for International Settlements, U.S. banks have more than $220 billion at risk through investments in German and French banks alone. If those firms start to topple, U.S. financial companies could as well, a hazard highlighted by the failure this fall of the MF Global brokerage firm because of its dealings in Europe.

The IMF, in a recent study of “spillovers” among the world’s major economies, noted that fallout from a deepening crisis among the euro countries would be felt most dramatically in the region itself, with the United Kingdom and Eastern European countries most at risk.

But the more deeply the problems spread to core nations such as France and Germany, the broader the impact, with risks to U.S. banks rivaling the crisis of three years ago.

“Core [euro zone] bank distress would . . . be a systemic event impacting banks globally,” the IMF study concluded.

The euro zone, Cliffe wrote, is “an omelette that cannot be readily unscrambled.”