So far, 18 states plus the District of Columbia have medical-marijuana laws, including Republican-leaning states like Arizona.

Support appears to have increased in Florida since 2011, when a pollster for Republican Gov. Rick Scott — who opposes medical marijuana — surveyed the issue. Pollster Tony Fabrizio found support was strong in Florida, 57-38 percent.

But passing a constitutional amendment in Florida is tougher than in many states, in large part due to the 60 percent threshold.

“If there was organized opposition and $5 million, you could beat this thing,” said John Sowinski, a long-time Florida citizen-initiative consultant. “Absent that money and organized opposition, this would have a good chance of passing.”

Sowinski noted that the proposal might be perceived as too broad. While it specifies certain ailments — from Alzheimer’s to Crohn’s disease to HIV/AIDS — but it also allows marijuana for “other diseases and conditions when recommended by a physician.”

Indeed, when the amendment is summarized without specifying the diseases, support falls 8 percentage points to 62 percent, when the ballot language is summarized for voters. Still, that’s 2 percentage points above the threshold needed to approve a Florida constitutional amendment.

“The weakness in the proposed amendment isn’t helping AIDS patients get medicine to cope with pain,” he said. “It’s the language that’s so broad it could allow doctors to simply recommend marijuana for almost anything. Many people still want drugs controlled.”

A plurality of Florida voters, about 49, percent say pot should remain illegal while about 40 percent say it should be legalized, the poll shows.

The pollster, Beattie, warned in his memo that the campaign should frame the effort in medical and personal terms; don’t say “legalize” and don’t say “drug.”

But, in another question, voters tacitly favored outright legalization when asked if marijuana should be regulated and taxed like alcohol and cigarettes; 68 percent favored it and 27 percent opposed.

Asked if marijuana should be a “ticketed offense like speeding or running a red light,” 48 percent approved and 42 percent disapproved, which is on the cusp of the poll’s 4 percent error-margin.

By a 41-34 percent spread, voters said pot was safer than alcohol. Those who said marijuana was a “gateway drug” to hard drugs like cocaine and heroin narrowly edged those who thought it wasn’t, 44-46 percent.

Potential opponents like the pharmaceutical industry, could be a good foil for the amendments backers.

When asked if they believed the pharmaceutical industry wants to keep marijuana off-limits to sell prescription drugs, “though marijuana could be a safer and cheaper alternative to some treatments,” 52 percent agreed. Only 30 percent disagreed.

Support for medical marijuana is weakest in the GOP-controlled Legislature.

For two years, the Florida House refused to hear a proposed constitutional amendment that would have allowed people to vote on the issue.

The plan’s sponsor, Democratic state Sen. Jeff Clemens of Lake Worth, said he plans this week to release conventional legislation — instead of a measure designed for voters — to decriminalize marijuana for medicinal purposes.