He said he plans to get that point across to lawmakers as well as voters in case the bill passes but is forced to referendum by opponents.
Six states and the District have legalized gay marriage, and Maryland is one of several states, including New Jersey and Washington, expected to consider bills this year.
The governor has been criticized for not taking a more active role last year in attempting to get the bill passed.
Delegate Emmett C. Burns Jr., a Baltimore County Democrat and minister, said gay marriage would undermine religion and that the only clergy members who support it are “quasi, fake religious leaders.”
“Don’t give me something I don’t want, then protect me from it,” said Mr. Burns, who is black. “It doesn’t work like that.”
Democratic leaders have estimated this month that they are still about three votes shy of a majority in the House. But Delegate Heather R. Mizeur said gay-marriage supporters have made progress and anticipate getting a majority.
Ms. Mizeur, Montgomery Democrat and one of seven openly gay delegates, said lawmakers intend to be more tight-lipped this year about vote counts.
She said supporters were perhaps too vocal last year, which enabled opponents to target lawmakers who were known to be undecided or waning in their support.
“We’re holding it closer to our chests,” she said. “But I personally have had some conversations where I know of some votes that are going to be coming.”