Women can be jailed for up to three years for having an illegal abortion while those who perform them face up to eight years in prison.
Jose Socrates, the Portuguese prime minister, called backstreet abortions a "national disgrace" in a video message posted on his Socialist Party's web site which urged voters to change the law.
"We want to change the existing law so that woman who have abortions can be accompanied by health centres and social services instead of by prosecutors and police," he said.
A poll published on Friday in the daily newspaper Jornal de Noticas found 38 per cent of likely voters intended to cast ballots in favour of changing the law, down from 53 per cent in a poll carried out for the paper in October when the government called the referendum.
The percentage of likely voters who intended to vote against the proposed change rose to 28 per cent from 21 per cent while the rest planned to abstain or were undecided, the survey found.
More than 50 per cent of Portugal’s 8.4m registered voters need to cast ballots for the referendum to be binding.
If the referendum is declared void because of low turnout, but the "yes" camp collects more votes than the "no" side, the government has said it will use its majority in parliament to alter the abortion law.
Around 8,000 demonstrators, according to police estimates, marched through the streets of the Portuguese capital, Lisbon, on Sunday in opposition to changes to the abortion law.
Some 10,000 women are hospitialised every year in Portugal because of
complications following illegal abortions, according to pro-abortion groups.
In a referendum held in 1998 voters, upheld the existing law by 51 per cent to 49 per cent, but the result was declared void as nearly seven out of 10 voters stayed away.