The Prime Minister, John Key, says he will support a bill to legalise gay marriage through its initial stages in Parliament, to allow full debate on it, but he won't yet commit to a final vote.
But Mr Key's deputy, Bill English, says the Government has other priorities and the proposed legislation is not that important. He says he thought the problem of gay marriage had been solved by civil unions.
Labour leader David Shearer says the bill reflects the reality of the times and he will be supporting it.
The private member's bill in the name of Labour MP Louisa Wall has been drawn from the ballot at Parliament, and when it comes before the House a conscience vote is expected. Mr Shearer says he expects it to get through.
The bill proposes changing the law to recognise marriage regardless of gender, sexual orientation or gender identity.
A generational issue, says MP
Ms Wall says many members of the gay community simply want the same rights and access to marriage that any other New Zealander has.
"I think this is a generational issue, to be honest," she says, "because 63% of New Zealanders support same-sex marriage but in the 18-to-24-year-old age group nearly 80% support it - so this is a bit of a challenge for those not Generation X-Y."
Ms Wall says her bill modernises the concept of marriage, and if it is passed, same-sex married couples will also be legally able to adopt children.
Green MP thrilled
The Green MP Kevin Hague says he is totally thrilled that the bill has been drawn from the ballot.
Although his own bill on same-sex marriage wasn't drawn, he says he's happy for Ms Wall all the same. He says they made a vow that whichever bill was drawn first, both of them would campaign for it, "so I'm looking forward to doing precisely that".
Mr Hague says he doesn't know if he and his partner of 30 years will marry if the law is changed to allow it.
Maori Party MP Te Ururoa Flavell says his party will also support the bill. But New Zealand First MP Richard Prosser says he will vote against it.
Mr Prosser says he has nothing against gays but believes in preserving the institution of marriage.
Other bills drawn
A bill from the Labour MP David Clark, which was also drawn, would raise the minimum wage to $15 an hour.
The State-Owned Enterprises and Crown Entities Amendment Bill, in the name of Labour MP Clayton Cosgrove, is also heading for a vote.
It proposes entrenching state-owned enterprises and would require a 75% majority in Parliament or a referendum in order to sell them.