As the U.S. government moves toward reclassifying marijuana as a less dangerous drug, there may be little immediate impact in the dozen states that have not already legalized cannabis for widespread medical or recreational use by adults.

But advocates for marijuana legalization hope a federal regulatory shift could eventually change the minds — and votes — of some state policymakers who have been reluctant to embrace weed.

"It is very common for a state legislator to tell me, 'Well, I might be able to support this, but ... I'm not going to vote for something that's illegal under federal law,'"...