It passed its second reading on May 25 and is due to return to the House tomorrow for its committee stages to be debated.
As the bill is still supported by a majority of MPs, the normal expectation would be that it would go through the committee stages, have its third reading and pass into law.
However, a provision in Standing Orders has the power to derail the wishes of most MPs and bring the bill to a halt. Standing Orders are the procedural rules which govern how Parliament and its committees operate.
Standing Order 326 provides that the House will not pass a measure if the Government certifies it does not concur "because, in its view, the bill, amendment or motion would have more than a minor impact on the Government's fiscal aggregates if it became law".
A government can only issue a financial veto certificate when a bill is awaiting its third reading, and must spell out its objections in detail. Provided it does that, a government can override a measure supported by a majority of MPs.
The Standing Orders do not spell out in dollar or percentage terms what "more than a minor" impact on the fiscal aggregates actually means. There is also no provision for a majority of MPs to challenge a financial veto certificate if they do not accept the Government's assessment of the impact of the proposals on the fiscal aggregates.
Governments normally use the financial veto to stymie amendments put up by MPs when the committee stages of bills are debated. This has been done 44 times over the past 20 years.
But what is proposed in relation to the paid parental leave bill is different. The Government has repeatedly said it plans to veto the entire bill, despite the fact it has majority support in the House.
This appears unprecedented. It is also anti-democratic. A majority supports the bill. The provisions have been thoroughly debated - they have been to select committee twice.
It is difficult to believe that the proposals would really have major financial implications for the Government, at a time when the Prime Minister is talking of $3 billion of tax cuts being on the horizon. The Government in last year's Budget announced the extension of paid parental leave from 16 to 18 weeks, and that took effect on April 1, 2016.
The cost of a further increase of eight weeks would be around $100 million - a fraction of the figure mooted for tax cuts.
The extension is also small in comparison to the Government's overall Budget for 2016: core Crown expenditure is set to be $74 billion this year.
New Zealand operates under a system of parliamentary sovereignty. This means Parliament has the right to make or repeal laws, and no other body has the power to override or set aside legislation. In almost all cases, laws are passed by a simple majority of members.
The financial veto provision in Standing Orders rides roughshod over that principle by allowing the Executive to disregard the wishes of the majority.
The democratic thing for the Government to do would be to accept that it is on the wrong side of parliamentary - as well as public - opinion and let the bill pass into law.
Catriona MacLennan is a barrister and former political reporter.