Prime Minister John Key will support the bill into law, and 15 National MPs planned to vote for it at least in its early stages. Cabinet ministers Judith Collins, Craig Foss and Chris Tremain added their support in the past week.
MPs from traditionally conservative electorates said they had been surprised by the responses from their constituents.
MP for Hunua Paul Hutchison, who was leaning towards opposing the bill, said: "Some churches came to me within an hour of the bill being drawn, and they were black-and-white about it.
"But I was quite amazed that quite a few individuals ... from mainstream churches, businesspeople, and farmers don't seem to be stressed by this particular one."
Nine MPs have confirmed they would oppose a change to marriage laws.
National MP Tim Macindoe said the purpose of the Civil Union Bill was to protect the legitimate legal rights of gay and de facto couples.
"In my opinion, if more protection is needed, it should be achieved by amending that legislation, not the Marriage Act."
Of the MPs who were undecided, 13 voted against civil unions in 2004, including Deputy Prime Minister Bill English.
New Zealand First leader Winston Peters originally suggested his party could abstain from voting and call for a referendum instead.
But it is understood that all eight party members will oppose the bill on Wednesday, because an abstention would mean it would require a smaller majority of 57 votes.
On Friday, the Human Rights Commission released a paper formally endorsing marriage equality and a non-discriminatory approach to adoption.
It said legal equality depended on New Zealanders having the right to found and form a family regardless of sexual orientation.
Ms Wall said the commission's paper also reinforced celebrants' right to refuse to marry same-sex couples, which was one of the churches' main concerns. She said she had spent a significant amount of energy debunking the myth that pastors would be jailed for refusing to marry gay couples.
Her bill would redefine marriage as a union of two people, "regardless of their sex, sexual orientation or gender identity". But it would not change the section of the Marriage Act which said marriage licences authorised, but did not oblige, celebrants to marry couples.
Anti-gay marriage lobbying was expected to intensify at the select committee stage, with Conservative Party leader Colin Craig promising a "research-based" campaign opposing the bill's passage. A Family First online petition opposing the law change has 40,000 signatures.