The money would be used to compensate the British and Dutch governments, which paid it out to 340,000 of their citizens who were hit when Icesave collapsed in 2008.
Observers say an Icelandic refusal to repay the money could block the remaining half of a $2.1bn International Monetary Fund (IMF) rescue package, as well as its EU and euro currency membership talks.
It could also damage Iceland's credit rating and destabilise the government, which negotiated the agreement in the first place.
The legislation was passed by parliament last year, but it went to a referendum after Olafur Ragnar Grimsson, the Icelandic president, refused to sign it into law because of huge public opposition.
Magnus Arni Skulason, a founder of the Indefence movement, which is opposed to the repayment deal, said the agreement being voted on was "obtained through coercion, with threats from both the British and the Dutch".
He also noted that most Icelanders felt the demanded 5.5-per cent interest rate was particularly unacceptable.
"You're basically sending the bill to tax payers for the failure of a private bank," he was quoted by the AFP news agency as saying.
But others argue the referendum is largely redundant as the terms of the repayment plan are already being renegotiated.
Johanna Sigurdardottir, the prime minister, described the referendum as "meaningless," saying she saw no reason to go to the ballot box.
Charlie Parker, a financial analyst with the Citywire website, told Al Jazeera: "When the referendum was originally conceived it was conceived in response to the first offer from Britain and the Netherlands to structure this repayment, of course that has since been revised."
But he also noted that Iceland had some "legitimate grievances", including that the UK and the Netherlands chose to repay all of their citizen's lost savings, even above the standard compensation limits.
"It was the government of Britain and the Netherlands that unilaterally decided they would pay back all the money that savers had invested," Parker said.
"I think Iceland can legitimately say 'if these governments made this decision unilaterally, why have we got to pay out for their largess to their citizens?'"
Jan Randolph, the head of sovereign risk at HIS Global Insight, told Al Jazeera there was no indication Iceland would not repay the debt, but that the referendum was about winning better terms.
"I think the referendum is really about bargaining position. The government will use the 'no' vote to come back to the British and the Dutch and say: 'Look, the people are not behind this, you've got to improve the terms further'."
Iceland's leaders have said they will resume talks to negotiate better terms with London and The Hague after the referendum.
Randolph told Al Jazeera: "The referendum is a chance for the Icelanders to vent their anger - their anger at their government and at Britain for using anti-terror laws to seize Icelandic bank assets, which accelerated the implosion of the banking system."
In the aftermath of the Icesave collapse, the UK invoked so-called anti-terror laws to take control of Landisbanki assets held in Britain. Icesave was the the online arm of Landisbanki.
First results from the referendum are expected shortly after polling stations close at 22:00 GMT, with final results later the same night.