Mr Robertson and Mr Sio were among a group of MPs who met conservative lobby group Family First on the steps of Parliament yesterday to accept a 48,000-strong petition calling for the bill to be scrapped.
New Zealand First was giving mixed messages about its voting intentions. But MP Brendan Horan suggested the party would oppose, not abstain.
"If there's a referendum in the bill, we'll support it. If not, I won't," he said.
Act Party leader John Banks confirmed he would vote for the bill at the first reading.
Mr Banks previously voted against Homosexual Law Reform and the Civil Union Bill. Asked why he was supporting it, he replied: "Because I am."
A large number of MPs have pledged their support to the first reading only, and their continued support depended on the debate at select committee. Among some concerns were how the law change would affect adoption rules and access to reproductive technology.
National MP Paul Hutchison, who opposed the bill, said: "We're in a situation where a gay individual can adopt, a gay couple cannot adopt. We haven't even talked about that kind of stuff and I think it's very important that we do."
Ms Wall said she hoped for an open, honest debate. "What I don't like is scaremongering and the fact that ministers are saying [they] will have to go to jail."
She was referring to a legal opinion from Family First which said church ministers and celebrants who refused to marry gay couples would be criminalised by the bill. This opinion went against a paper released last week by the Human Rights Commission.
Ms Wall: "They will retain all the rights that they currently have ...my bill isn't going to affect them in any way."