"But not under this miserable National Government. That's not what's going to happen.
"For the first time in this Parliament's history, a bill is about to have a third reading debate and there will be no vote put at the end."
National MP Mark Mitchell said the Government was showing fiscal responsibility by vetoing the legislation.
He highlighted the measures National had implemented for children, including a lift in benefit payments for the first time in 30 years and raising paid parental leave from 14 weeks to 18 weeks.
"I could never buy into the argument that just because a parent had got 18 weeks instead of 26 weeks... they are not able to bond with their child," he said.
The bill was also opposed by the Act Party.
Leader David Seymour said he was proud to oppose the bill, which he described as political grandstanding by Labour.
Bringing up children was a "20-year enterprise", he said.
"The idea that the only thing between children growing up healthy and well-adjusted in New Zealand is simply the problem that they don't have funding for an extra six weeks is simply not true."
Once the debate was over, Labour made a desperate bid to salvage something from the bill.
Attempts to have Finance Minister Bill English hauled into the debating chamber to explain his veto were unsuccessful.
Several MPs attempted to put their party votes on the official record, but were denied leave by the Speaker.
On Tuesday, Mr English was accused by Ms Moroney of exaggerating the costs of an extra eight weeks of paid parental leave.
In an interview with Radio New Zealand, the minister had said it would cost $280 million more a year.
He admitted in Parliament that he meant to say $280 million over four years - as stated on his financial veto.
