Marijuana use in both states continues to be illegal under the federal Controlled Substances Act. One option is to sue the states on the grounds that any effort to regulate marijuana is pre-empted by federal law. Should the Justice Department prevail, it would raise the possibility of striking down the entire initiatives on the theory that voters would not have approved legalizing the drug without tight regulations and licensing similar to controls on hard alcohol.

Some law enforcement officials, alarmed at the prospect that marijuana users in both states could get used to flouting federal law openly, are said to be pushing for a stern response. But such a response would raise political complications for President Obama because marijuana legalization is popular among liberal Democrats who just turned out to re-elect him.

“It’s a sticky wicket for Obama,” said Bruce Buchanan, a political science professor at the University of Texas at Austin, saying any aggressive move on such a high-profile question would be seen as “a slap in the face to his base right after they’ve just handed him a chance to realize his presidential dreams.”