Even if it gets majority support in Parliament, Labour's proposed members bill on paid parental leave could be vetoed by the Government.
Parliament's rules allow the Government to veto any legislation it views as having more than a minor impact on its finances.
The Government says an extra $150 million a year for the scheme is too expensive.
But Labour says that would not be the total cost, as the Government would receive some tax back from the parental leave payments, and it would save on childcare subsidies.
The bill proposes to increase paid parental leave from the current 14 weeks to 26 weeks by 2014.
The Labour Party says a veto would be an extreme move to make.
The bill is being promoted by Labour MP Sue Moroney and she says the power to exercise a financial veto is not one for any Government to use lightly.
But the Government does have the power to veto the bill at its third reading, as long as it outlines specific reasons for doing so.
However, the Labour Party is confident the bill will have enough support to pass its first reading in Parliament, though two parties have yet to declare whether they will back it.
The bill has been drawn from the parliamentary members ballot.
The National and ACT parties are not supporting it because they say it is unaffordable.
ACT leader John Banks says the country is cash strapped and business are struggling, so it does not make sense to incur the additional cost at this time.
However Ms Moroney believes the legislation will have the numbers to pass its first reading without National and ACT.
She says the bill has the support of the Green and Mana parties and Government support partner United Future.
The bill's fate at its first reading now hinges on the backing of New Zealand First and the Maori Party. The parties will discuss the bill at their next caucus meetings.
United Future leader Peter Dunne, who has campaigned to extend paid parental leave, says the bill is a move in the right direction. "I certainly think that the debate should be held."
Paul Mackay of Business New Zealand told Morning Report that extending paid parental leave raises the question of how the extra money will be found.
"If we're going to extend it - and nobody's saying we shouldn't - we should make sure we do it in a way where we know we can foot the bill and not unbalance the other things that we want to pay for, like early childhood education, for instance.
"We don't want to take out of another pot to pay for this."
Council of Trade Unions president Helen Kelly said New Zealand lags other countries in paid parental provisions and Business New Zealand's lack of support is disappointing.
