In a referendum held in 1998, voters supported upholding the existing abortion law by 51 per cent to 49 per cent, but the result was declared void as nearly seven out of 10 voters stayed away.
Surveys have suggested that as many as 45 per cent of voters could fail to cast their ballots this time making the outcome difficult to predict.
Opposition to the changes in the law has largely been led by the church in a country where 90 per cent of people consider themselves to be Roman Catholic.
Cardinal Jose da Cruz Policarpo, the Patriarch of Lisbon, has repeatedly said that Catholics must oppose abortion.
"Whatever the motives that justify this dramatic act in the eyes of a woman, it is always the denial of a place in the world for a human life that was conceived," he said in his televised Christmas Eve address to the nation.
Those campaigning against the referendum have also argued that a vote in favour of lifting the ban will increase the number of abortions, raise state health costs and give momentum to easing other laws such as gay marriage.
If low turnout voids the outcome of the referendum, but the "yes" camp collects more votes than the "no" side, the Socialist government has said it will use its majority in parliament to alter the law.
The "yes" campaign has focused on the estimated 23,000 secret abortions carried out every year. Jose Socrates, the prime minister, has called them "Portugal's most shameful wound" and argued that legalising abortion will end such back-street operations and allow women proper treatment.
Under the current law, women who are caught performing abortions can be jailed for up to three years - although most trials have ended in suspended sentences or acquittals.
Many Portuguese women who wish to terminate a pregnancy simply go across the border to Spain where abortions have been allowed for more than a decade.