A second poll, conducted by the Alco firm found an even higher majority in favour of a deal with Europe: 57 against 29 percent.
While Greeks had been worried about taxes and wages, they are now confronted by banks being closed and restrictions on cash withdrawals, measures that would only worsen if Greece does leave the eurozone.
This may help ensure a majority for a 'Yes' vote. But Natixis's Waechter warned the difficult situation that Greeks faced means "we need to make sure this malaise doesn't get transformed into a rejection of Europe."
Nobel prize-winning economist Paul Krugman believes that Greece's bailout partners -- the troika of the EU, IMF and ECB -- intentionally pushed Tsipras into a corner with their bailout proposal.
"This is, and presumably was intended to be, an offer Alexis Tsipras, the Greek prime minister, can't accept, because it would destroy his political reason for being," Krugman wrote in an op-ed in The New York Times.
"The purpose must therefore be to drive him from office, which will probably happen if Greek voters fear confrontation with the troika enough to vote yes next week."
A referendum thus suits Europeans if it provokes the fall of Tsipras and his anti-austerity Syriza party.
Negotiations could then be restarted with a new government, likely made up of technocrats.
"The government is committed to carry out the will of the people" as expressed in the referendum, Greek Finance Minister Yanis Varoufakis said Saturday.
If the Greek people "want that we sign (the bailout agreement), we'll do it, even if it takes a reshuffle or different government," he said, suggesting a Syriza exit from power if there is a 'Yes' vote.
- Delay or default -
With a 'Yes' vote in hand, the EU, IMF and ECB could then move to undertaking short-term measures to keep Greece's financial system from collapsing while negotiations on a deal resume.
EU leaders have said the door remains open to Greece, although German Chancellor Angela Merkel made clear that negotiations could only be resumed after the referendum.
The ECB, while it refused on Saturday to increase aid to Greek banks, did not completely shut down the programme, meaning it could provide the help needed for them to reopen.
Greece will likely miss its 1.5-billion-euro ($1.7-billion) payment due to the IMF on Tuesday, but the significance of this will depend a lot on the outcome of the referendum, said Bruegel Institute economist Nicolas Veron.
"In the event of a 'No' vote Greece will not be able to honour its obligations on a permanent basis, whereas today it is just not able to do so on a temporary basis," he said. "It is the difference between a payment delay and a payment default."
While the creditors hold the cards needed to reach a deal, the question is whether they will play the one that would solve Greece's debt problem and possibly help swing a 'Yes' vote.
Euler Hermes chief economist Ludovic Subran said he believes "Europeans need to make a concession" and offer "to restructure Greek debt" even though there is no guarantee this will ensure a 'Yes' vote.
But eurozone countries, which now own most of Greece's debt, have been reluctant to promise to write off the debt as it would likely have political repercussions in several countries.