Sponsors of proposed constitutional amendments are required to submit 766,200 valid petition signatures to get on the November ballot.
Petitions are submitted to county election supervisors, who verify the signatures and report the information to the secretary of state.
The lawsuit seeks an extension until Feb. 1 to submit signatures to county supervisors, with the deadline for verification similarly extended.
Those regulations included requiring petition gatherers to register with the Department of State and receive petition forms from the agency.
The state had tallied 219,290 valid petition signatures from Make It Legal Florida as of late Tuesday afternoon, according to the Division of Elections website.