“Quite frankly, I don’t think we are ready, or want to go down that road,” Dannel P. Malloy, the Democratic governor of Connecticut, which has legalized medical marijuana and decriminalized possession of small amounts of marijuana, said in an interview. “Perhaps the best way to handle this is to watch those experiments that are underway. I don’t think it’s necessary, and I don’t think it’s appropriate.”

The hesitance expressed by these governors reflects not only governing concerns but also, several analysts said, a historically rooted political wariness of being portrayed as soft on crime by Republicans. In particular, Mr. Brown, who is 75, lived through the culture wars of the 1960s, when Democrats suffered from being seen as permissive on issues like this.

“Either they don’t care about it as passionately or they feel embarrassed or vulnerable. They fear the judgment,” said Ethan Nadelmann, the founder of the Drug Policy Alliance, an organization that favors decriminalization of marijuana. “The fear of being soft on drugs, soft on marijuana, soft on crime is woven into the DNA of American politicians, especially Democrats.”

He described that sentiment as, “Do not let yourself be outflanked by Republicans when it comes to being tough on crime and tough on drugs. You will lose.”