If Prime Minister George Papandreou's new government fails to get the necessary parliamentary support in a midnight vote Tuesday, it would throw into question whether it can pass a new austerity bill by the end of the month as demanded by international creditors.
Greece is being kept financially afloat by euro110 billion ($157 billion) EU-IMF bailout fund.
A default by Greece could spark a financial maelstrom around the world, dragging down Greek and European banks as well as stoking renewed fears over the finances of other eurozone countries, such as Portugal, Ireland and Spain.
Expectations that Papandreou would win lifted world markets. His Socialist party holds a five-seat majority in the 300-member legislature, and a simple majority is needed to pass.
"Indications over the last 24 hours or so have certainly been that the government will survive, if only because the alternative would be so dire," said Beat Siegenthaler, an analyst at UBS.
Papandreou reshuffled his Cabinet last week and replaced his finance minister to ease growing dissent within the governing party.
On Tuesday the new finance minister, Evangelos Venizelos, promised that parliament will pass the unpopular austerity package by the end of June in order to comply with European Union demands to receive the next payment in its bailout loan.
Venizelos said Parliament is set to vote on euro28 billion ($40.2 billion) worth of budget cuts and other savings next week.
Greece has said it will face a default unless it receives the euro12 billion ($17.3 billion) rescue loan installment from European countries and the International Monetary Fund.
"We must follow this course to save the country," Venizelos said.
"Our European partners ... face is with distrust," he said. "This is an atmosphere that we have to change."
Papandreou's popularity has been hammered by the latest austerity measures, with an opinion poll published Tuesday giving the Socialists a 20.1 percent approval rating. Rival conservatives faired marginally better, at 21 percent, in the GPO survey for private Mega television of 1,000 adults. No margin of error was given.
Some 7,000 protesters, chanting "thieves! thieves!" were gathered outside parliament, while a strike by the country's powerful electricity workers' union continued to cause rolling blackouts for a second day.
Socialist skeptics, however, appeared to shy away from another fight.
Prominent dissenter Nikolas Salagiannis, said he would vote in favor of the government following the cabinet reshuffled.
"This has generated a slim hope that the issues can be addressed ... We back the new government," Salagiannis said. But he added: "Make no mistake, our connection with people in the street and in the squares is dwindling by the day. We have gone from austerity to more austerity, from denial to denial to get where we are ... and the public's tolerance has been used up."
Though considered unlikely, if Papandreou loses Tuesday's vote he would have little choice but to call early elections or try to form a coalition government. However, all opposition parties have said they want elections.
But even after winning, he faces an even more difficult task: Getting parliament to back the new austerity measures as well as an unpopular euro50 billion ($71 billion) privatization program by the end of the month.
If the new austerity measures pass, the finance ministers of the 17-nation eurozone will meet July 3 to give Greece its next bailout installment.
A key requirement from the eurozone and the IMF is that Greece steps up its privatization drive.
European officials are also discussing a second, similar-sized bailout for Greece since it's obvious the country won't be able to return to the bond markets and raise money to pay creditors any time soon.
"I trust that the new Greek government will receive the confidence of parliament," European Commission President Jose Manuel Barroso said after meeting with Papandreou Monday, but added the crucial vote was the one on the new austerity package.
"I therefore trust that Greece's elected representatives will back these measures next week in a spirit of national and indeed European responsibility," Barroso said. "These choices are not easy, but nor are the problems that need to be addressed. Now is not the time to falter."
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Menelaos Hadjicostis and AP photographers contributed.
