Paid parental leave would be extended to 26 weeks under legislation that will go before Parliament later today - with supporters urging National not to use a veto should the bill get the required numbers.
Labour MP Sue Moroney hosted upbeat supporters, many with their own young children, at Parliament today ahead of the first reading of her members bill.
It would extend paid parental leave to 26 weeks.
• Counting the cost of going back to work
This year the Government increased paid parental leave from 14 to 16 weeks. A further lift to 18 weeks is due next year.
Labour, NZ First, the Greens, and the Maori Party will vote in favour of Ms Moroney's bill, meaning United Future leader Peter Dunne will have the deciding vote.
He has previously expressed support for 26 weeks, but has refused to say which way he will vote. Ms Moroney told supporters today she was confident of his support.
"His track record has been very good and I fully expect that he will continue to support it. I can't think of a rational reason why he would not."
However, even if the bill passes its readings, it could still be defeated if Finance Minister Bill English invokes a financial veto, as he has previously threatened to do because of the expense.
Ms Moroney's Paid Parental Leave Bill was one of four drawn from the member's bill ballot in July and follows on from a similar bill she put up in the last Parliamentary term.
She had enough support to pass that last term - which would have forced National to use its financial veto to block it.
However, after the 2014 election National and Act had just enough votes to vote it down and it was defeated in February.
NZ First leader Winston Peters' win in the Northland byelection means National has one fewer vote and NZ First has one more, so Ms Moroney has enough support to pass it again if Mr Dunne continues to support it.
Rebecca Matthews, a spokeswoman for parental leave lobby group 26 for Babies, formed after an earlier unsuccessful bill was introduced by Ms Moroney, said they had common ground with National.
"Neither of us want them to use a financial veto...last time they delayed Sue's bill until after the election, so they wouldn't have to use an unpopular and undemocratic veto. This time, that [delaying] probably won't be an option.
"National have already recognised the benefits of increasing paid parental leave. And, again, we will show them how popular and sensible a policy this is."
Ms Matthews said if the push for 26 weeks' of paid leave was successful she looked forward to their lobby group being renamed 52 for Babies.
Ms Moroney, speaking above gurgles and occasional screams from some audience members, said babies went through significant milestones between 18 and 26 weeks, and parents should have the chance to share those.
"You might not have noticed, but we've had the all-powerful Finance and Expenditure Select Committee just waltz past us while we have been talking - that's where the debate is going to be had about funding this initiative."