“I think it’s a real act of desperation,’’ he said. “They’re trying to pull a rabbit out of a hat. Shame on the mayor.”

Dolphins executives say their focus groups show public support for the financing plan, given Ross’ pledge to keep public dollars below 50 percent of the work.

Ross’ fellow NFL owners are expected to vote May 22 to award the 2016 and ’17 Super Bowls. Miami Gardens and Santa Clara, Calif., are vying for 2016, and the loser will take on Houston for 2015.

With an upgraded Sun Life better able to attract Super Bowls, national college football championships and global soccer, team executives are pushing the renovation as a boost to tourism. The Greater Miami Chamber of Commerce last week endorsed the plan, following a non-binding vote by the Miami-Dade County Commission embracing the proposal, too. The University of Miami’s new athletic director, Blake James, has been making the rounds in support of the plan to upgrade the Hurricanes’ home field, as have leaders of the Orange Bowl committee.

Sen. Braynon would alter his bill to allow the higher Miami-Dade hotel tax if approved by voters, according to the source familiar with the Dolphins’ lobbying effort. The move would give Miami-Dade the highest hotel tax in the state. State lawmakers would still need to change state law to allow the tax hike and for the new $3 million yearly subsidy for Sun Life.

Sun Life currently receives $2 million a year, tied to renovations made in the 1990s when the Florida Marlins played baseball there. At the time, Wayne Huizenga owned both teams.

Dolphins executives and Gimenez declined to comment Saturday. On Saturday night, Gimenez’s office announced a joint press conference with team CEO Mike Dee. Braynon declined to talk about the bill, but said he and others have pushed the Dolphins to allow a referendum. When he announced the proposed financing plan on Jan. 14, Ross said the pending Super Bowl decision left no time for a vote.

But the Dolphins faced a tough road in Tallahassee on their tax-hike bill, given the tax-averse, Republican-controlled Legislature. Last week, Miami-Dade lawmakers caucused to agree on the county delegation’s priorities, and the stadium bill did not make it onto the list. The Dolphins feel confident that the referendum provision will make the bill much easier to pass, a source close to the team said.

A majority of county commissioners, however, endorsed the legislation on Jan. 23 — and tasked Gimenez with negotiating with the Dolphins to avoid a deal lopsided in the team’s favor, as critics say happened with the publicly financed ballpark for the Miami Marlins. Gimenez was elected mayor after stridently opposing the Marlins deal while a county commissioner.

The mayor’s calendar shows he met on Jan. 28 with Dolphins CEO Mike Dee, and on Feb. 1 with Ross.

Last month, Gimenez said he would welcome a public vote on the Dolphins’ plans.

“I think they probably should go to referendum, but do we have the time? I don’t know,” he told The Miami Herald on Jan. 17.