An opposition member's bills on same-sex marriage and another on public holidays are due to progress further through the House on Wednesday.
The bills, both sponsored by Labour MPs, are likely to get enough support to become law.
The Holidays (Full Recognition of Waitangi Day and Anzac Day) Amendment Bill in the name of Labour's David Clark will have its second reading.
It would transfer Waitangi Day or Anzac Day public holidays to Monday if they fall on the weekend.
The National Party caucus will not vote for the legislation, but Mr Clark says it will have the numbers to pass.
National also considered whether or not to use a veto on the bill, which is available to the Government if a member's bill would have an economic impact on its books.
The Prime Minister John Key said the Government would not be using the veto on the Holidays Bill.
The Marriage (Definition of Marriage) Amendment Bill will also have its second reading on Wednesday night.
The bill in the name of the Labour MP Louisa Wall amends the Marriage Act so that two people - regardless of their sex, sexual orientation or gender identity - can marry.
It passed its first reading with 80 votes to 40, in a conscience vote, and the Ms Wall says she's relatively confident those numbers will remain solid.
She said says all indications are the bill has a high level of support among the broader public.