22 March 2013 Last updated at 00:02 ET
Many Cypriots are concerned they may lose their jobs and life savings, and there have been sporadic clashes outside parliament
MPs in Cyprus are due to begin voting on a series of bills that aim to raise the funds the country needs to secure an international bailout.
The country is in a race against time after the European Central Bank gave Cyprus until Monday to find the money.
If it does not, liquidity to the country's banks could be cut off and they could collapse.
Many Cypriots express fears they are set to lose their savings, and there have been long queues at cash machines.
"The next move may prove its salvation or destruction," warned the Bank of Cyprus, the country's largest - itself said to require urgent funding to prevent collapse.
It said the Cypriot economy was "on the brink".
Parliamentarians flatly rejected a plan to tax bank deposits earlier this week.
They need to find 5.8bn euros (£4.9bn; $7.5bn) to qualify for a 10bn-euro bailout loan from the EU and International Monetary Fund (IMF).
Continue reading the main story “Start Quote
The country is surviving on a lifeline from the European Central Bank”
End Quote Critical timeAfter holding a phone conference on Thursday night to discuss the situation, eurozone finance ministers said they stood "ready to discuss with the Cypriot authorities a draft new proposal", which they expected "the Cyprus authorities to present as rapidly as possible".
Political leaders discussed the options with President Nicos Anastasiades on Thursday, and the package was then discussed by the cabinet. But MPs said they needed more time to study the nine bills that make up the draft legislation.
If no "Plan B" can be found by Monday, the ECB may cut off funding to the island's banks, it said in a statement, triggering their collapse and possibly the country's exit from the euro.
Anxiety is growing as the country - and the eurozone - enter a critical few days, says the BBC's Mark Lowen in Nicosia.
The country's two biggest banks, Bank of Cyprus and Laiki, are believed to be reliant on the ECB's Emergency Liquidity Assistance, provided via the Central Bank of Cyprus.
All Cypriot banks have been shut until next Tuesday to prevent mass withdrawals, but long lines have been forming at cash machines.
They are still dispensing cash but with such demand are frequently running out, and on Thursday Laiki radically lowered the daily withdrawal limit to 260 euros.
Continue reading the main storyAt the scene
Mark Lowen BBC News, Nicosia
The fear is catching. Outside cash machines, queues have grown all day with savers worried about their money - particularly in the two most troubled banks. Rumours that they might be closed altogether only sparked more concern.
Elsewhere, businesses are demanding payment in cash, turning away credit cards for fear they won't get their money. It's led to a drop in business - with customers staying away.
This is the price Cyprus is paying for its current crisis. And the race is on to resolve it by next Monday when the European Central Bank says it will turn off its emergency funds. On Tuesday the banks will have to open here and that is when the queues could multiply unless a credible plan has been formed and Cyprus has raised its share of the bailout.
The coming hours are critical to save this troubled country and calm an anxious eurozone.
"There are rumours that Laiki Bank will never open again. I want to take out as much as I can," retired government official Phaedon Vassiliades told AFP news agency as he withdrew cash at a machine in the capital, Nicosia.
"I have nearly 60,000 euros as savings in this bank and some credit societies. I don't know if I will ever get it back now. This is what I had and now it seems it is all gone."
"We are doomed. Our sunny days are over," said Neophytos Constantinides, an insurance company employee.
Earlier crowds gathered outside parliament in anticipation of a vote on "Plan B" - a key component of which is the establishment of a state "investment solidarity fund" which would issue bonds on state assets to raise the 5.8bn euros required.
Other elements of "Plan B" could include restructuring other Cypriot banks, use of pension funds, and accepting an offer of help from Cyprus' wealthy Orthodox Church.
A revised levy on deposits also remains a possibility.
It might also contain some kind of Russian help. Cypriot Finance Minister Michael Sarris is in Moscow discussing possible assistance - along with the head of the European Commission, Jose Manuel Barroso.
Big Russian investors are believed to hold about a third of all Cypriot deposits - and reacted with fury when the initial plan to tax deposits by up to 9.9%.
But the chairman of the Eurogroup of eurozone finance ministers, Jeroen Dijsselbloem, told the European parliament that Moscow had indicated it was not willing to extend "another loan or an investment in the banks", Reuters news agency reported.
He also told MEPs he doubted that there was really a possible Plan B - and he partially defended the original idea of a levy on deposits, saying "alternatives would have made Cyprus' debt unsustainable".
Reports suggest Moscow could consider buying interests in recently discovered offshore gas reserves.
But analysts point out that any revenue from such discoveries remains years off, and unnamed Turkish officials have been quoted as saying Ankara - which lays claim to some of the gas - would challenge any such arrangement.
The banking sector dominates Cyprus' economy and if a viable rescue is not organised soon the island state risks having to abandon the euro.
Cypriot banks were among the bondholders who had to take a big "haircut" in the second massive bailout for Greece.
Since 2008 the eurozone has been badly bruised by the massive bailouts provided for Greece, the Republic of Ireland and Portugal. There is a widespread reluctance to commit more EU taxpayers' money to ailing banks in southern Europe.
