Mr Peters called for a referendum to be held on same-sex marriage.
"Serious issues like this should be decided by the public of this country, and not a few temporary, empowered politicians."
He would not give a direct answer when asked whether New Zealand First MPs would choose to abstain.
If the party did opt out, the bill would need only 57 votes to pass.
The Herald poll showed this number was well within reach.
But if New Zealand First did vote, its members are likely to oppose it.
One of the party's MPs, Richard Prosser, has previously said he would vote against it, and two others, Mr Peters and Barbara Stewart, voted against civil unions in 2004.
Five other MPs - National MPs Chester Borrows, Phil Heatley, Colin King, Eric Roy and Mike Sabin - say they would oppose a law change.
Mr Borrows said he had "faith-based reasons" for opposing the bill.
Mr King said: "What my wife and I have enjoyed over 42 years, I don't think anybody else of the same sex could enjoy."
All MPs from the Green Party, the Maori Party, Mana, United Future and most Labour MPs said they supported the bill at least at the first reading.
Eight National MPs, including Prime Minister John Key and Cabinet ministers Paula Bennett and Hekia Parata, have also backed the bill.
But because some Labour MPs were likely to vote against it - Clayton Cosgrove, Damien O'Connor and Ross Robertson did not vote for civil unions - a few more National votes would probably be needed to push the bill into the committee stage.
Thirty-seven National MPs have not made their mind up on the bill.
Most of them said they had not read it, or were seeking responses from their constituents.
National MP Shane Ardern said he was opposed only to churches being required to act against their beliefs - something Ms Wall has said would not happen.
"But if it's just a case of giving some kind of legal status that they don't already have, then I wouldn't oppose that," Mr Ardern said.
THE NUMBERS
Are you for or against Louisa Wall's bill?
* 52 - For
* 13 - Against
* 2 - Undecided / maybe for
* 2 - Undecided / maybe against
* 44 - Undecided
* 8 - No reply / no comment.