After early signs that agreement on a new national unity coalition could be reached quickly, the drive by the socialist and conservative parties to create a government that will rule only until February appeared to be losing momentum.
So far they have agreed that a "100 day" coalition should be set up to push a 130 billion euro ($180 billion) bailout for Greece through parliament and that elections should be held in February.
But after days of wrangling, no one knows who even will lead this government.
"A national unity government, right now," Ethnos daily said on its front page. "The country and the society cannot endure this anymore."
European Union politicians expressed their alarm in Brussels about how debt crises in Greece and Italy are shaking international confidence.
"Europe is running dry on credibility and a solution to a high debt crisis must be lower debt. The responsibility for that falls with the country with high debt and that is obviously Greece and Italy," Swedish Finance Minister Anders Borg said.
Greece has repeatedly made promises to deal with its huge budget deficit and debt, only to break them later, leading to exasperation in Brussels and EU demands that the new government spell out in writing precisely what it will do.
If Greece pushes through its euro zone bailout, it will indeed lower its debt but not by exercising budget discipline. Instead, the bailout envisages a bond swap which will halve the value of banks' holdings of Greek government debt.
The opposition New Democracy party acknowledged the pressure to name a government leader. "The issue of the Prime Minister must be resolved immediately ... we are waiting for the announcements," the state ANA news agency quoted New Democracy spokesman Yiannis Mihelakis as saying.
Ordinary Greeks also demanded a new government, replacing a socialist administration which descended into chaos.
"If this government doesn't work out, we are lost," said Panagiotis Dimitriadis, 80, a public sector pensioner.
Dimitriadis has already had his pension cut as the outgoing government imposed austerity demanded by Greece's international lenders, but he is still trying to help out his son and seven grandchildren.
Prime Minister George Papandreou and New Democracy chief Antonis Samaras agreed on Sunday that the coalition should be formed, but little else.
Monday came and went without any accord on who will lead the coalition, despite a former vice president of the European Central Bank, Lucas Papademos, emerging as a frontrunner.
"Today is the last chance for the two main parties," center-left daily Ta Nea said in an editorial. "They have to come up with a government strong enough to take the country out of the shifting sands of a political impasse that leaves us defenseless, at the mercy of the crisis. Time is up."
The cabinet will hold an emergency session on Tuesday.
Frustration was also apparent in Brussels where officials said the new government had to show it was serious about implementing promises Athens has made to its EU and IMF lenders in return for the bailout agreed last month.
"It is essential that the entire political class is now restoring the confidence that had been lost in the Greek commitment to the EU/IMF program," said EU Economic and Monetary Affairs Commissioner Olli Rehn.
Papandreou caused chaos last week by calling a referendum on the bailout, a vote which would probably have rejected the package because of the austerity measures tied to it. Papandreou backed down, but was forced into agreeing to make way for the unity coalition.
Weary of broken promises from Athens, Rehn said the coalition must "express a clear commitment on paper, in writing, to the EU/IMF program."
The stakes could not be higher. Greece faces bankruptcy in December when big debt repayments are due, unless it can get hold of more emergency funding soon. For the euro zone, it is a question of credibility with international financial markets.
For two years it has labored to solve the problems of Greece, a very small part of the bloc's economy, leading to doubts about how it would manage if the debt crisis engulfed the far bigger Italian or Spanish economies.
What is now a regional crisis could hit the global economy if it goes unchecked, and the United States weighed in with a demand that Greece live up to its responsibilities. "We urge the government to move as quickly as possible to fulfill the commitments," said White House press secretary Jay Carney.
Papademos remained a frontrunner for prime minister, although European Ombudsman Nikiforos Diamandouros, who handles complaints against EU institutions, and Greece's envoy to the IMF, Panagiotis Roumeliotis, were also mentioned as potential candidates.
An aide said the Greek economist, who left the ECB last year, had arrived in Athens on Monday from the United States where he is a Harvard academic.
Papandreou has been in touch with Papademos, a senior government official told reporters.
Papademos oversaw the nation's adoption of the euro in 2002 as Bank of Greece governor before moving to the ECB, and is a well-known figure in European capitals.
Some Greek media speculated that he was setting tough conditions, demanding greater powers than Papandreou or conservative leader Antonis Samaras were prepared to give.
A source at the New Democracy party, which Samaras leads, said it would support the new government but wanted no cabinet posts.
Current Finance Minister Evangelos Venizelos, a member of the PASOK socialist party, could stay in his post for the sake of continuity, said the source, giving the first indication of who would occupy any of the cabinet posts.
New Democracy would back the 2012 budget and a bond swap plan contained in the bailout package, under which the value of banks' holdings of Greek government debt would be halved.
However, PASOK had to hand certain major ministries -- including any involved in running next February's elections -- such as justice, the interior and even defense to non-party technocrats, he said.