Thirty-two MPs had not decided which way they would vote.
Just one MP, New Zealand First's Richard Prosser, said he would definitely oppose it, but a handful more indicated they were likely to oppose it on the grounds that their constituency was conservative on issues of homosexuality.
Ms Wall said she was confident of the bill's passage into law because she had the support of Prime Minister John Key, Opposition leader David Shearer, and the majority of the public.
But she expected "an array of views" from New Zealanders if it reached the committee stage.
Mr Key has previously indicated he would support the bill at first reading.
However, Finance Minister Bill English said the bill was "not that important" and "we are focusing on jobs and the economy".
Asked what he thought of the premise of gay marriage, he said he felt "the problem had been solved" with civil unions.
Ms Wall said New Zealand was following a global shift towards marriage equality, with Australia, the United States and Britain all considering changes to marriage laws.
"At the end of the day I hope that it becomes about what marriage means in modern society.
"So for me, it's about if two people love each other, and marry and commit to each other for the rest of their lives, it should be something we all celebrate."
She stressed that religious institutions would not be forced or compelled to marry same-sex couples.
"Churches can choose to continue to define marriage as they want. This isn't about the state changing the religious definition. But what the state [does] do is give out licences."
If her bill passed into law, couples who were in a civil union would be able to dissolve it and transfer to a marriage. While the finer points of the law would be worked out at committee stages, it was expected that married same-sex or transgender couples would be able to adopt children or get access to reproductive technology.
Some MPs said they had changed their minds on the marriage issue. Maori Party co-leader Tariana Turia said she had voted against civil unions in 2004 but now felt it was important that couples had a choice.
"So long as children have the best parents that they can have who value them and love them, then that's the most important thing, rather than their sexuality."
THE VOTES
Do you support Louisa Wall's bill?
41Yes
2 Undecided but
leaning towards yes
32 Undecided
1 No
76 Total