The Greeks have already reduced their deficit by five percentage points of the gross domestic product, “unprecedented cuts in a modern economy,” Mr. Tilford said. “But the cuts have had a much stronger negative impact on the economy than the troika imagined, and fiscal austerity has pushed the economy deep into recession. Debt can only be paid out of income, and that means growth.”

Greece does not have access to many tools to fight recession, like devaluing its currency or cutting interest rates, at least as long as it remains a member of the euro zone. Its monetary policy is controlled by the European Central Bank.

Some independent economists accept that Greece has no choice but to try a fresh round of cuts. Edwin M. Truman of the Peterson Institute for International Economics in Washington said Greece had to go through more pain because it had run a budget deficit even before making payments on its debt, meaning it needed loans to pay off its loans.

Only after Greece reorganizes its budget, tax collection and labor market and is running a surplus — not including interest payments on the debt — can economists begin to calculate how much in debt payments Greece is actually able to afford, and then figure out how big a debt restructuring it needs.

“As long as they’re running a primary deficit, they need to keep tightening the belt,” Mr. Truman said. “Rescheduling now doesn’t relieve Greece of the burden of fixing the economy to create a surplus.”

It is not getting any easier. In the year since its first bailout, Greece has cut $17 billion through across-the-board wage cuts, layoffs and attrition in its bloated state sector, which employs 800,000 people, a quarter of the Greek work force. But given its recession, the economy shrank and tax revenues fell, meaning that Greece did not meet the original target of a government deficit of 9.1 percent of G.D.P. as agreed with its foreign lenders, prompting them to demand more cuts.

European demands have placed Mr. Papandreou in an increasingly untenable position. He must sell the increasingly restive Greek people on more austerity with no clear signs of recovery. And he has to persuade his Socialist Party on reforms that undo almost everything the party has stood for in the past.