Defeat for the government this week would send ripples of anxiety right across the eurozone On Monday, Mr Papandreou said only his 28bn-euro (£25bn) austerity programme would get Greece back on its feet.
If the government loses, the EU and IMF could withhold 12bn euros of loans and Greece could run out of money in weeks.
French President Nicolas Sarkozy has said French banks are ready to offer new 30-year loans to Greece when its current debts fall due.
He said other European countries whose banks had lent money to Greece were considering the same model to help prevent a default. But the UK denied it was pressing banks to "take a haircut".
'Massacre' More than 5,000 police officers are due to be deployed in the centre of Athens on Tuesday morning, when tens of thousands of striking workers are expected to march towards parliament at 1000 (0700 GMT).
The general strike will disrupt or halt most public services, with doctors, ambulance drivers, journalists and even state-funded actors taking part.
What went wrong in Greece?
- Greece's economic reforms, which led to it abandoning the drachma as its currency in favour of the euro in 2002, made it easier for the country to borrow money.
Airports will be shut for hours at a time, with air traffic controllers walking out between 0800 and 1200 (0500-0900 GMT) and 1800 and 2200 (1500-1900 GMT). Ferries, buses and trains will also stop running.
The unions are angry that the government's austerity programme will impose taxes on those earning the minimum wage, following months of other cuts which have seen unemployment rise to more than 16%."These measures are a massacre for workers' rights. It will truly be hell for the working man. The strike must bring everything to a standstill," Thanassis Pafilis, a Greek Communist Party MP, told the Associated Press.
Some protesters have said they will encircle the parliament building to prevent MPs from entering. The austerity package and implementation law must be passed in separate votes on Wednesday and Thursday.
If the measures are passed, the next instalment of Greece's 110bn-euro bailout will be released by the European Union and International Monetary Fund.
European officials will also start to finalise the details of a second bailout - worth an estimated 120bn euros - designed to help Greece pay its debts until the end of 2014.
The BBC's Chris Morris in Athens says defeat for the government this week would sends ripples of anxiety right across the eurozone, with Greece facing the prospect next month of becoming the first member state to default on its debts.
'Flawed' plans As the debate in parliament on the austerity measures began, the prime minister warned a defeat would mean the national "coffers" would be empty within days and urged MPs to do their "patriotic duty".
Mr Papandreou added: "I call on Europe, for its part, to give Greece the time and the terms it needs to really pay off its debt, without strangling growth, and without strangling its citizens."
The new Finance Minister, Evangelos Venizelos, acknowledged that the cuts were "unfair" but said they were absolutely necessary.
He urged parties to work with the governing Panhellenic Socialist Movement (Pasok) because it would help build "greater national strength".
But the main opposition leader, Antonis Samaras of the New Democracy party, said the thinking behind the austerity package was flawed and that tax rates should be lowered rather than raised in order to stimulate the economy.
The outcome of the debate is uncertain. Mr Papandreou faces opposition from within Pasok, with two MPs saying they may oppose the bill.
The party has a slim majority, with 155 seats out of 300 in parliament.
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