LONDON — Eighteen months into a sovereign debt crisis — and after many futile efforts to resolve it — the endgame appears to be fast approaching for Europe.

While its leaders may well hold to the current path of offering piecemeal solutions, nervous investors are fleeing European countries and banks.

Two main options exist: either the euro zone splits apart or it binds closer together.

Each of these paths — Greece, and possibly others, dropping the euro or the emergence of a deeper political union in which a federal Europe takes control of national budgets — would lead to serious political, legal and financial consequences.

But with financial panic now threatening to move beyond Italy and Spain to Belgium, France and Germany, the euro zone’s paymaster, the pressure to arrive at a solution is at a new level of intensity.

In Britain, even the satirical weekly Private Eye has weighed in, proposing last week that the answer was for Europe itself to leave the European Union.

Underlying these possible outcomes has been Europe’s persistent inability to address the central weakness of its common currency project: how to get money from the few countries that have it, mainly Germany and the Netherlands, to the many that need it — Greece, Italy, Spain, Portugal, Ireland and perhaps even France.

The consequences of continued inaction are dire. Uncertainty and austerity have decimated the euro zone’s growth prospects, and analysts now expect the region’s economy to shrink 0.2 percent next year — a blow for the many American companies that export there.

American financial institutions are also at risk. According to the Institute of International Finance, they have $767 billion worth of exposure through bonds, credit derivatives and other guarantees to private and public sector borrowers in the euro zone’s weakest economies.

With the European Central Bank continuing to refuse to print money as its counterparts in the United States and Britain have done, investors now foresee a much greater likelihood of a broad market crash and a worldwide recession.

Such anxieties were on display last week when Vítor Constâncio, the vice president of the central bank, gave a speech to investors in London.

It was billed as an address on the international monetary system, but given the circumstances, there was little interest among investors in Mr. Constâncio’s views regarding fixed versus floating-exchange rates and quite a lot about what steps the central bank might take to address the crisis.

One somewhat frantic investment banker noted that beyond the Italians and the Spanish, even the Germans were having problems selling their bonds. What, he asked, was the European Central Bank going to do about it?

Mr. Constâncio mentioned the central bank’s bond buying program and making loans available to banks, but he was blunt in saying that unless countries like Greece and Italy followed treaty rules and reduced their budget deficits, there was not much the central bank could do.

“The countries must deliver,” said Mr. Constâncio, a former governor of the Portuguese central bank. “In the end, it is governments that are responsible for the euro area — it is not just the E.C.B.”

It is this eat-your-spinach policy approach, however, that many analysts now say is making the situation worse as countries throughout the euro area — including Germany, the region’s economic locomotive — cut spending and raise taxes to meet budget deficit targets.

In a recent paper, Simon Tilford, an economist at the Center for European Reform in London, argues that imposing additional rules rather than creating a federal framework to allow the euro zone to commonly transfer or borrow money — as can be done in the United States — will end in disaster.

“The solution to the problem has become the problem itself,” he said. “And investors see this: you cannot just keep cutting spending in the teeth of a recession.”

Bernard Connolly, a persistent critic of Europe, estimates it would cost Germany, as the main surplus-generating country in the euro area, about 7 percent of its annual gross domestic product over several years to transfer sufficient funds to bail out Europe’s debt-burdened countries, including France.

That amount, he has argued, would far surpass the huge reparations bill foisted upon Germany by the victorious powers after World War I, the final payment of which Germany made in 2010.

Analysts say it is the unbending attitude of Germany, Europe’s richest country, that it not become responsible for the debts of weaker economies that has so far stymied progress on the widely supported idea of a euro area able to issue its own bonds.

Lack of movement on a federal Europe has pushed investors to consider what would happen if a country like Greece exited the euro zone. Analysts predict dire consequences for the departing country, ranging from default to a collapse of its banking system.

A recent report by UBS estimated that in the first year, the citizens of the exiting nation would face costs of as much as 11,000 euros a person on top of the austerity-induced pain already incurred.

Such a move might be legally impossible: there is no provision in any European treaty for a country to leave or be expelled from the euro zone — a conscious choice by the framers of the project.

But if a country made such a decision, it would have to leave the 27-member European Union as well, thus entering a more profound state of exile.

A view is now taking hold among many European leaders that the ever-worsening crisis may result in Brussels being given direct control over the budgets of countries that continue to run excessive deficits — a proposal made recently by the euro’s most passionate advocate, Jean-Claude Trichet, former president of the European Central Bank.

“The will to make this thing work is stronger than you might think,” said Larry Hatheway, an economist at UBS and one of the authors of the report on the cost of one or more countries leaving the euro zone.

In this vein, several economists at Bruegel, a research institute in Brussels, are calling for a euro zone finance minister, elected by the European Parliament, who would have limited federal powers to raise revenue.

This is a radical measure, to be sure. Not only would it challenge the sovereignty of nations, but it would also require time and treaty changes.

With time short, pressure is building on the European Central Bank to defy German objections and buy more distressed government bonds, but there is little indication the bank has decided to do so.

Last week, Mr. Constâncio actually appeared to boast about the bank’s restraint thus far, explaining to harried investors that the central bank’s bond-buying effort represented about 2 percent of euro area G.D.P. That compares with an intervention of 11 percent of G.D.P. by the Federal Reserve in the United States and 13 percent by the Bank of England.

“We are not financing the deficits of countries,” he said.

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