The survey, released Friday just ahead of the final campaign rallies, also found that 76 percent of Greeks want to stay among the 19 nations using the euro currency.
Asked whether holding the referendum was a good idea, 42 percent said yes while 48 percent said it was a mistake.
The poll was carried out July 1-3.
Meanwhile, the eurozone's financial rescue fund — officially Greece's largest creditor — says it considers the country to be in default, even though Athens has not missed a repayment to the fund itself.
The European Financial Stability Fund said Friday it considered Greece's failure to cover a 1.6 billion-euro ($1.8 billion) repayment this week to the International Monetary Fund to be an "Event of Default" that allows the EFSF to activate a loan repayment demand.
Fund CEO Klaus Regling says "this event of default is cause for deep concern. It breaks the commitment made by Greece to honor its financial obligations to all its creditors, and it opens the door to severe consequences for the Greek economy and the Greek people."