This is Ms. Gregoire’s final year in office (she has decided not to seek a third term), and many people have speculated that she is supporting same-sex marriage only now that the political risk of doing so has diminished. But the governor said her position had evolved, in part through conversations with her two daughters.

“They’ve grown up with kids who’ve got two moms and two dads, and they just think this generation needs to get over it,” she said.

The governor said she had been preparing to address the issue this session since the fall.

“In the middle of the night, I’d wake up and come up with an argument I heard and I would work through that argument,” she said. “I think I’ve attacked straight on any argument that has been advanced on the subject. You can respect the rights of the churches to decide who they will marry, but at the same time you can’t sit here as governor and have somebody come into an office say, ‘I want a license,’ and say, ‘No, we’re going to discriminate. We’re from the state.’ ”

The Washington bill is modeled on the law passed by New York last summer, which included language clarifying that religious groups and churches are not required to marry same-sex partners.

Senator Ed Murray, a Seattle Democrat who is chairman of the powerful Ways and Means Committee, has been one of the most persistent advocates for same-sex marriage in the Legislature. Mr. Murray said Ms. Gregoire strengthened protections for religious groups beyond what he had proposed to her.

Some of the same lawmakers who led opposition to the state’s “everything-but-marriage” law and supported the referendum to defeat it say they will organize a coalition to defeat a marriage law, should this bill pass the Legislature. On Friday, a group of Roman Catholic bishops in Washington issued a statement opposing the new bill and praising the state’s existing law for recognizing “the unique and irreplaceable potential of a man and woman to conceive and nurture new life, thus contributing to the continuation of the human race.”

Mr. Murray, noting that Washington’s petition-friendly political system makes any bill passed by the Legislature vulnerable, said he and others had worked since last spring to build support behind the scenes, anticipating a battle in the Legislature but also at the polls.

“I’m a little concerned that people are popping the Champagne corks,” he said. “They need to remember it took us years to find one vote on the civil rights bill and we’re several votes short on the marriage bill. We’re very close, but we don’t have the votes yet.”