Labour's numbers at the last election estimated that the policy would cost an extra $80 million in the first two years, $372 million over four years, and $700 million over six years.
Labour says the financial veto has been used rarely but National issued research from the parliamentary library showing that Labour had exercised the veto 31 times over the nine years it was last in Government.
The bill, the Parental Leave and Employment Protection (Six Months' Paid Leave) Amendment Bill, has been introduced but not yet debated.
A veto can be exercised at the third reading if the Government deems it would have more than a minor impact on its finances.
But if New Zealand First opposed the bill at any stage, it would be defeated. Mr Peters said the NZ First caucus has not yet discussed the bill. The party has voted in the past for extensions to paid parental leave, though in happier fiscal times.
"The Government keeps crying poor and cutting social services yet it can pour billions into failed finance companies for its mates so perhaps a compromise can be reached," Mr Peters said.
Ms Moroney said Mr English's promise to veto the bill showed not only a disregard for the will of Parliament but smacked of arrogance.
Meanwhile, Plunket and the early childhood teacher union, NZEI, weighed in behind the bill.
NZEI national executive member Hayley Whitaker said the bill was long overdue and it suggested that the cost of extending leave could be offset by the resulting reduction in subsidies to early childhood education services.
"We know that the current limit of 14 weeks paid leave means that many families suffer financial stress, and feel they have no choice but to return to the workforce before they are ready to."
A Plunket spokeswoman said the organisation believed that the bill deserved to be debated.
"Babies need the chance to bond with their mum without pressure on her to return to work or manage on a suddenly reduced income."
Mr English has said the Government was still $10 billion off clearing its overdraft and if the bill passed it would have to be funded through borrowing.
He believed the public would have a similarly "pragmatic" approach.
THE DEBATE
* 14 weeks' to 26 weeks' paid parental leave is proposed.
* $150 million a year is what the 14 weeks currently costs.
* The bill has been introduced but not yet debated.
* National has said it will veto the bill if it needs to.