A Field Poll from April showed 56 percent of the state’s registered voters in support of legalizing and taxing marijuana for recreational use to fill some of the budget deficit. Mr. Schwarzenegger told reporters at a fire-safety event in Davis, Calif., that he did not support sweeping legalization, but that more information would help.

Marijuana advocates said the governor’s invitation to have a discussion at all was a landmark.

“What stands out about Gov. Schwarzenegger’s comment is not that he thought it, but that he said it,” said Ethan Nadelmann, executive director of the Drug Policy Alliance. “There has been enormous fear at a political level about saying out loud and on the record that we should think about this.”

Assemblyman Tom Ammiano, Democrat of San Francisco, introduced legislation in February that would legalize the cultivation and sale of marijuana for recreational use. Mr. Ammiano’s proposal has been shelved this session, but he has said he would reintroduce it next year. Sales could raise $1.2 billion to $1.34 billion in annual tax revenue, some estimates say.

But that would be little salve for the state’s deficit, which could reach $20 billion in 15 months if ballot initiatives proposed by the governor do not pass, said Assemblyman Chuck DeVore, Republican of Irvine. Mr. DeVore said he did not support legalizing marijuana, and was surprised to hear the governor’s comments.

“I think this shows the governor’s growing desperation over the budget,” Mr. DeVore said.