Hamilton workers and women's advocates have given the thumbs up to a push to increase the period of time new mothers can get financial support from 14 to 26 weeks.
Yesterday afternoon 26 for Babies, a group campaigning in support of an extension to paid parental leave, delivered the first batch of postcards to the prime minister calling on him not to veto the bill.
However, the chances of Sue Moroney's Parental Leave and Employment Protection (Six Months' Paid Leave) Amendment bill being passed into law appear doomed, with Prime Minister John Key having announced earlier this year that the Government will simply veto it.
Parliament's rules allow the Government to veto any legislation it views as having more than a minor impact on its finances.
At present, paid parental leave costs about $154 million a year.
The Government's estimates of the cost of the legislation change would be an additional $68 million in 2014-15, $143 million the following financial year and rising to more than $166 million by 2018-19.
However, those figures are disputed by the bill's supporters, who say 26 weeks was the optimum time for giving babies the best possible start in life while allowing time for mothers to get used to the demands of parenting, without the added pressures of having to return to work to make ends meet.
The bill has already been through the select committee stage and is due to return to Parliament for its second reading in early September. The Government cannot exercise a financial veto on a bill until it gets to its third reading.
Ms Moroney, a Hamilton-based Labour list MP and the party's women's affairs spokeswoman, said about 4000 people and organisations had sent submissions to the government administration select committee, which reflected the great level of interest in the legislation.
It would be arrogant of the Government "to just shoot it down", she said.
She understood finance minister Bill English had received official advice that the most it would cost would be about $285.6 million during three years.
"It is certainly not going to cost anywhere near as what the Government is saying. There are many ways of bringing in cost savings.
"We initially had wall-to-wall opposition from employers groups on this, but most of them have come around. They can see how it is from the mums' perspective."
Megan Morris, the president of the Hamilton-based Young Workers' Resource Centre presented one of the submissions to Parliament on the bill.
She said she was dismayed to hear it was likely to be vetoed.