Alexis Tsipras, the Prime Minister of cash-strapped Greece, is expected to present new proposals to an emergency euro zone summit on Tuesday, under pressure from European leaders to come up with credible ideas as his country's banks face a potential meltdown.
With Greek lenders down to their last few days of cash and the European Central Bank tightening the noose on their funding, Tsipras must persuade the bloc's other 18 leaders, many of whom are exasperated with five years of crisis, to open negotiations fast on a new loan to rescue Greece.
The leaders of Germany and France, the currency area's two main powers, said after conferring on Monday that the door was still open to a deal to save Greece from plunging into economic turmoil and ditching the euro.
But Chancellor Angela Merkel, under pressure in Germany to cut Greece loose, made clear it was up to Tsipras to come up with convincing proposals after Athens spurned the tax rises, spending cuts and pension and labour reforms that were on the table before its 240 billion euro bailout expired last week.
European Commission President Jean-Claude Juncker, under suspicion from both sides for trying to broker a last-minute deal, told the European Parliament: "There are some in the European Union who openly or secretly are working to exclude Greece from the euro zone."
He did not name names but may have been referring to German finance minister Wolfgang Schaeuble, who has made no secret of his scepticism about Greece's fitness to stay in the euro.
From the Greek side, the key to making any deal politically acceptable will be to win a stronger commitment from Merkel and other lenders to reschedule Greece's giant debt burden, which the International Monetary Fund says is unsustainable.
Without some firmer pledge of debt relief, neither Greece nor the IMF is likely to accept a deal. But that may be more than Germany and its northern allies can swallow.
"The door is open to negotiations, but there isn't much time left and the situation is urgent both for Greece and for Europe," French President Francois Hollande said in a joint media appearance with Merkel in Paris.
At stake at the emergency summit beginning at 6pm (1600 GMT) in Brussels is more than just the future of Greece, a nation of 11 million that makes up just 2% of the euro zone's economic output and population.
If Greek banks run out of money and the country has to print its own currency, it could mean a state leaving the euro for the first time since it was launched in 1999, creating a precedent and fuelling doubts about the long-term viability of an incomplete European monetary union.
"Even if it did not trigger a short-term domino effect, the integrity of the euro zone would come under fresh threat with each episode of political uncertainty within member countries," said Thibault Mercier, an analyst at BNP Paribas.
Strengthened by the overwhelming 61.3% 'No' vote in Sunday's referendum, the leftist Tsipras won the unprecedented support of all other Greek party leaders on Monday and replaced his abrasive finance minister Yanis Varoufakis with the soft-spoken negotiator Euclid Tsakalotos.
"They (creditors) wanted a 'Yes' to prevail so they could humiliate the Greek prime minister, to go weakened, under these conditions of funding asphyxiation, and be a pushover. That didn't happen," labour minister Panos Skourletis told Antenna TV.
In an intensive round of telephone diplomacy, Tsipras spoke to the heads of the ECB, the IMF and the European Commission, as well as Merkel, Russian President Vladimir Putin and US treasury secretary Jack Lew.
But he gave little clue of what reform concessions he would make to try to convince deeply sceptical European leaders to lend Athens more money after five months of acrimonious and fruitless negotiations with his leftist administration.
His proposals were not expected to go much beyond a letter he sent to euro zone partners last week, acccepting most of the terms of a creditors' offer that was no longer on the table, but still seeking some loopholes for social or coalition reasons.
The United States, China and Japan all called for a solution in which Greece stays in the euro zone. Juncker told EU lawmakers in Strasbourg he was working night and day to get negotiations reopened but he chided the Greeks for their confrontational approach, saying it was unacceptable to accuse the EU of behaving like "terrorists", as Varoufakis did last week.
"Throwing Greece out of the monetary union or indeed the European Union is not something we want or indeed should want," said the EU's chief executive, who was heckled by leftists and Eurosceptics when he said Greeks hadn't been properly informed about what they were voting on.
European Central Bank policymaker Ewald Nowotny suggested the bank might be able to provide some sort of bridge funding while Greece negotiated a longer-term conditional loan to see it over a crucial July 20 bond redemption to the ECB.
Greek newspapers dramatised the make-or-break nature of the Brussels showdown.
Centrist daily Ethnos headlined: "Time has run out for a solution before catastrophe," while the centre-right Eleftheros Typos said: "Tsipras' games finish at today's council: Time of crisis: deal or Grexit."
Greek newspapers said the proposals would be based on ideas that Juncker put forward at the end of June with a few tweaks and would not differ much from the last plans presented by Athens itself last week.
Euro zone national officials were irritated that Juncker had gone beyond the agreed negotiating mandate of the three creditor institutions in his last-ditch diplomacy, and it is not clear that they will be more receptive to his ideas now.
A clear majority of Greece's 18 partners favour a hard line at the summit, arguing that they too are democracies and that Greeks should not get easier money because they had rejected the austerity terms, casting further doubt on whether they would implement any reforms agreed now.
The ECB left unchanged its emergency liquidity lifeline for Greek banks but raised the discount it charges on collateral they have to present for funds - a measure banking sources said was largely symbolic since the total they could borrow was capped.
A bank closure in force since the talks collapsed was prolonged until Thursday at least, and cash withdrawals remain limited to 60 euros a day, with 20 euro notes running out.
The Athens stock exchange was also ordered closed for two days in Tuesday and Wednesday to throttle speculation. Even with the country on the brink of economic collapse, Greek newspapers reported the government was still seeking exceptions from its reform pledges for special interests.
Athens wants to keep a 30% discount on value added tax on Greek islands and protect defence spending from cuts, which rightist junior coalition partners the Independent Greeks have called "red lines".