The Miami Dolphins’ sprint to get public funding to upgrade Sun Life Stadium got a boost Wednesday when Miami-Dade County commissioners urged Florida lawmakers to pass a bill designed to create new state and local subsidies for the renovation.

The Dolphins are asking for an increase in Miami-Dade’s mainland hotel tax to 7 percent from 6 percent and for a $3 million-a-year subsidy from the state. Their goal is to get the government to fund about half, or $199 million, of a $400 million renovation that would revamp jumbo monitors, move seats closer to the field and build an open-air canopy that would keep fans drier and cooler.

For the county to increase the hotel tax, it needs a thumbs-up from the state. Then, to bump the tax up it must come back to the county for a vote.

The Dolphins say they need the renovations to lure more national college football title games and Super Bowls to South Florida, particularly the National Football League’s 50th championship in 2016. To get the premier NFL showcase game, the Dolphins must compete with San Francisco’s new stadium, and the team’s bid would have to be in place by the end of May.

The County Commission’s vote Wednesday was a nonbinding request. But state lawmakers pushing the Dolphins’ proposal said they wanted local support to lobby a divided delegation.

And commissioners still suffering the public backlash over the one-sided deal to build the Miami Marlins’ Little Havana ballpark had a hard time ignoring the 300-pound gorilla in the room.

There was plenty of discussion about the football club opening its books, diversity in hiring and fair negotiations. But almost every speech on the dais began with a reminder of the Marlins fiasco.

“The stench of the Marlins deal is in the pores of everything this is about,” said Commissioner Esteban “Steve” Bovo, who also said he was concerned the commission might be rushing to judgment because most residents aren’t aware of the Dolphins’ plan.

The discussion began with Dolphins Chief Executive Officer Mike Dee explaining the financing plan and saying a vote in favor of the resolution “would send an important message to our lawmakers statewide.”

Before taking his seat among the dozen or so Super Bowl and Orange Bowl committee members who tagged along with him, Dee warned commissioners a “no” vote could stop all dialogue, “and potentially sets this community back 10 years or more” because Miami-Dade, in his view, would lose the ability to host major concerts and football and soccer games.

At the end of almost two hours of discussion, commissioners voted 9-4 in favor of the resolution, and told Mayor Carlos Gimenez to begin negotiating with the Dolphins immediately. Gimenez catapulted to office in large part because of his stubborn, aggressive stance against the Marlins deal. Former Mayor Carlos Alvarez was recalled partly because of his support for the ballpark.

“I look at what the Dolphins have on the table as the starting point. And when I go buy a car, I never pay full price,” said Gimenez.

Chairwoman Rebeca Sosa and Commissioners Bovo, Javier Souto and Xavier Suarez voted against the measure. Voting in favor were Vice Chairwoman Lynda Bell and Commissioners Bruno Barreiro, Jose “Pepe” Diaz, Audrey Edmonson, Sally Heyman, Jean Monestime, Dennis Moss, Juan C. Zapata and Barbara Jordan, who sponsored the measure.