Cannabis advocates say a new survey shows the drug could be on track to become legal but a narrow margin makes the outcome uncertain.
Opinion polls had shown support for the bill - being voted on in a referendum - dropping over this year - down to as low as 35 percent in late September.
The new poll, conducted by UMR and commissioned by the Helen Clark Foundation and the New Zealand Drug Foundation, found 49 percent in favour and 45 percent against.
Green supporters (82 percent), Māori respondents (66 percent), people aged 18-29 (62 percent) and Labour supporters (62 percent were more likely to say they would vote for the Bill.
National supporters (26 percent) and respondents over 60 (33 percent were less likely to say they would vote for the Bill).
Helen Clark Foundation chief executive Kathy Errington told Morning Report the margin was narrow and voter turnout would dictate the outcome.
Support had gone up a "negligible" one point since its last poll in July, she said, and getting out to vote "really does matter".
"Polls are uncertain and it's very hard to poll on referenda issues - you can't use previous elections as a model, you can't easily project turnout - all we know for certain is the polls have indicated that it's close, or this poll certainly has," she told Morning Report.
"I personally wish that this had not gone to a referendum because this is an issue with so much stigma, so much shame for the 'yes' side. The people who care the most about this result are people who are struggling with their drug use and want to do differently and want to change.
"But it's very hard to come out in the media and say you're a regular cannabis user. You're confessing to a crime and you're also confessing to something which many people are ashamed of.
"That's why, instead of those people whose voices should be leading this debate, there's proxies like me or the Drug Foundation who have to talk about why this policy doesn't work... and has damaged so many people for so many years and has achieved nothing."
New Zealand Drug Foundation director Ross Bell said polls have proven to be a poor predictor of recent overseas referendum results.
Legalisation of cannabis in the US states of Colorado or Washington was passed by a wider margin than in polls, Errington said, indicating some people may be reluctant to tell pollsters what they think.
The online survey of a representative sample of 1129 New Zealanders 18 years of age and over was carried out between 22 September and 5 October.
Read more about the 2020 election: