Overall, in Moreno’s survey, nearly 61 percent of people polled strongly oppose the measure, while nearly 12 percent simply oppose it. Only 17 percent support or strongly support it.

Poisoning the Dolphins effort: the unpopular Miami Marlins baseball stadium deal, which led to the recall of former Miami-Dade Mayor Carlos Alvarez, Moreno said.

“These are recall numbers,” he said. “What they tell you is Miami-Dade County has not yet recovered from the Marlins deal. And I think people are very reluctant to give public money to a private sports team.”

Dolphins vice president Nat Moore on Wednesday subtly brought up the Marlins, without naming the ball club, during a Wednesday appearance at the Greater Miami Chamber of Commerce.

“If every time you did one bad business deal, you decided to never do another deal, you’d go out of business,’’ Moore said. “Don’t hold anything against our deal.”

Moore received big applause when he mentioned Wednesday’s approval by the Senate Finance & Tax Committee.

The Dolphins are asking for the mainland hotel tax to increase from 6 percent to 7 percent, as well as up to $90 million in sales-tax subsidy rebates, paid out over 30 years. The $3 million annual sales-tax break would be in addition to $2 million in annual payments SunLife Stadium is already receiving.

Altogether, taxpayer money would help fund about half of the costs for the $400 million renovation.

A key point for the Dolphins: The ownership, including Palm Beach billionaire Steve Ross, is paying for more than half of the cost of the improvements. The team is a Miami icon. Also, the Dolphins say, the NFL will be less likely to host a Super Bowl in Miami Gardens if the old stadium isn’t improved.

Miami-Dade’s legislative delegation hasn’t made the Dolphins stadium a priority bill.

The Dolphins stadium isn’t a must-pass bill for the House speaker or Senate president, neither of whom is from South Florida. And lawmakers from outside South Florida have relatively little incentive to spend time and energy on a measure like this during a 60-day lawmaking session where they have a short window of time to get their bills passed.

Also, a majority of legislators are Republican, and many worry about votes that could allow potential conservative opponents in a primary to attack them for casting votes that allow taxes to rise — even though these taxes would be paid by hotel guests and fans at the stadium, not by rank-and-file taxpayers.

Meanwhile, In Miami-Dade, the Dolphins effort might have already done political damage. Moreno’s poll shows that 49 percent of likely voters believe the county is on the wrong track, while about 28 percent think it’s on the right track.

“That sentiment is partly a result of the Dolphins plan,” Moreno said. “By going to the commission and getting support for this, it really soured people’s view of the county. It looks like business as usual.”

Moreno, who has polled for Miami-Dade Mayor Carlos Gimenez, said he had simple advice for lawmakers: “Don’t support this.”

Gimenez said he has his doubts about the Dolphins deal as his administration negotiates with the club.

“These numbers don’t surprise me,” the mayor said. “The Marlins deal is the elephant in the room. It poisoned any effort like this for any future sports franchise. Before this poll, we didn’t even know if we were going to reach an agreement with the Dolphins. Now the path is even tougher.”

Miami Herald staff writers Doug Hanks, along with Herald/Times staff writers Mary Ellen Klas and Steve Bousquet, contributed.