Attorney General Pam Bondi, House Speaker Will Weatherford and Senate President Don Gaetz want the court to keep the initiative off the ballot. The justices will listen to both sides Thursday.
Supporters are gathering petitions to put the amendment on the ballot. So far more than 136,000 signatures have been verified. More than 683,000 are needed to put the issue before voters.
Bondi has called the wording of the amendment misleading — which is one of the reasons the court can keep it off the ballot.
A Quinnipiac University poll last month showed 82 percent of voters support medical marijuana.