The policy is expected to cost about $270 million a year once fully implemented. Labour has estimated about 59,000 households will benefit from the payment in a baby's first year.
About 63,000 families earning less than about $80,000 will continue to receive some level of payment for a further two years at abated rates.
Labour's children's spokeswoman, Jacinda Ardern, said the poll result showed the policy had broader support than simply among Labour voters.
"It suggests it has appeal to a broad range of voters. There are obviously some swinging voters in there who consider the package is positive."
She did not believe the initial explanatory hiccup had impacted on it.
Labour scored 29.5 per cent in the poll and the combined Labour-Green vote was 43 per cent.
National's Economic Development Minister, Steven Joyce, said Labour should be disappointed by the result.
"Generally if you say to people, 'Here's something that will give you more money', they tend to support it more positively.
"Possibly what's changing is people realise it's all money that has to come from somewhere, and they'd expect those sorts of policies to be more targeted rather than all the way up to $150,000."
Mr Joyce said it was possible that support among women was lower because they had looked at the fine print more closely.
Ms Ardern said although the package came at a cost, it would pay off in the longer term by taking financial stress off families in the first year of a baby's life.
The payment was one of the recommendations of the Children's Commissioner's Expert Advisory Group on Child Poverty. The poll of 750 voters was taken from March 6 to 16 and has a margin of error of 3.6 per cent.
