There is no secret about the tab coming due — Greece will need more than $40 billion over the next year or so to keep itself afloat and avoid what European officials consider their nightmare scenario, a default by one of the countries that use the euro.

But deciding who will pay has left European, International Monetary Fund and Greek officials locked in another round of crisis talks as they try to figure out a series of tough issues. How hard should Greece’s citizens be pushed for further cuts in social programs and other concessions? How much of the bill should shift to taxpayers from other European countries? Should investors in Greek bonds — including Europe’s major financial institutions and the European Central Bank itself — take a hit?

After confronting the issue — that the government of Greece has promised far more than its economy can deliver — for a year and a half, each side is wary of giving more.

Greek officials face a restive population already absorbing high unemployment and a loss of retirement and other benefits without any clear payoff in terms of economic growth. Possible losses at major banks or at the ECB, which has bought tens of billions of dollars in Greek bonds as part of a rescue effort, have led officials to all but rule out imposing losses on bondholders. Turning Europe into a “transfer union” — where taxpayers in economically healthier countries pay for the less well off — is politically difficult.

Yet a resolution is important to more than Greece.

In a presentation at the IMF last week, Mark Cliffe, chief economist for the ING Group, outlined the stakes if Greece were forced to leave the 17-member euro currency union. He projected a quick loss of about 10 percent of the country’s economic output and a broad shock to the financial system that would leave the rest of the euro area and the United States in a new recession.

That’s the incentive pushing negotiators toward a second Greek bailout.

The discussions are being monitored carefully by the Obama administration and others concerned that a misstep could upend Europe’s financial system or trigger problems in Spain or other larger and heavily indebted countries.

Stock markets have seesawed in recent weeks on little more than rumor about the outcome, dropping last week when top European officials suggested private bondholders may be asked to accept losses, rallying Tuesday when a program seemed near.

Talks are continuing this week, with an IMF team analyzing where Greece stands. Top European officials are heading to Athens to meet with Prime Minister George Papandreou about his plans for cutting spending, selling off state assets or other steps to accelerate the country’s economic restructuring.

“Greece is insolvent,” Cliffe said. “The question is who is going to pick up the bill. It’s distributional politics.”

It’s a problem Europe and the IMF thought had been resolved when they set up a three-year, $150 billion bailout for Greece last year. That was supposed to “catalyze market access,” according to the program, and allow Greece to borrow money on its own by reassuring investors that the country could meet its obligations.

But over the past year, the country’s economic plan has slipped, the interest rates demanded by investors to hold Greek bonds have soared and talk has revived of a possible default. Even more starkly, concern is rising about a possible exit by Greece from the euro area so it could reclaim more control over its economic policy and reestablish its own currency.

The IMF has said it won’t release about $4.5 billion under the existing bailout unless it is clear that the rest of the developing shortfall in Greece’s finances is covered by other means, such as further budget cuts or asset sales, more in loans from other European nations, or some contribution from existing bondholders.

But there’s little certainty about the longer-term outcome. Three European countries have had to borrow money from their neighbors and the IMF this year, and none has shown clear signs of the projected economic revival.

Analysts at Moody’s Investors Service on Wednesday issued their latest in what has become a steady series of downgrades to Greece, saying they now consider it a 50-50 likelihood that the country will default.

A year into its economic restructuring, the country remains saddled with “highly uncertain growth prospects and a track record of underperformance,” Moody’s said.