The Miami Dolphins and local tourism officials presented the National Football League on Tuesday with the most expensive Super Bowl bid in South Florida’s history, but the team’s CEO said amped-up entertainment options won’t be enough if voters don’t approve a subsidized renovation of Sun Life Stadium.

An upgraded stadium “is the only impediment between us and success,’’ Dolphins CEO Mike Dee said in a telephone press conference after a closed-door meeting in New York with NFL executives over the region’s Super Bowl bid. “We have a beautiful home with a rusty fence.”

South Florida’s Super Bowl Host Committee expects to spend about $21 million in private and public funds putting on the kind of Super Bowl outlined in the thick binder presented to NFL executives in New York. The confidential proposal includes creating a Super Bowl theme park in downtown Miami, including closing down Biscayne Boulevard, constructing a “Hail Mary Zip Line” along the waterfront and possibly mooring barges to accommodate some of the action, according to interviews and leaked details about the plans.

“We were impressed by the feedback,’’ Rodney Barreto, the chairman of the local Super Bowl committee, said after the NFL meeting. “We were applauded.”

This week, the NFL met with the three metropolitan areas pursuing Super Bowls 50 and 51 before final bids are due May 7. South Florida and the San Francisco area are competing for the 50th game in 2016, and the loser will take on Houston for the 51st game in 2017.

The Dolphins have used the prize of hosting the 50th Super Bowl as a reason to rush approval of a subsidized renovation of Sun Life. Earlier this month, Miami-Dade scheduled what is believed to be the quickest election in its history in order to have voters consider raising hotel taxes for the upgrade in a May 14 referendum, seven days before NFL owners will award the 50th and 51st games at a May 21 meeting in Boston.

Under a deal approved by Miami-Dade Commissioners, the Dolphins would only be eligible for county stadium funds if the NFL awards the county a Super Bowl before June 1. While County Mayor Carlos Gimenez had initially negotiated language that specified an award of the 50th or 51st Super Bowl, the Dolphins asked for a more broad requirement after NFL executives balked at formally linking a specific game to stadium subsidies.

After the change, Gimenez warned he would not be happy if the NFL tried to award South Florida a game in 2018 or beyond as a way to satisfy the requirement. But in remarks Tuesday, Dee said there was no talk by NFL executives of how South Florida might host a Super Bowl after 2017.

The stadium push has complicated South Florida’s latest Super Bowl bid. With the Dolphins asking for a hotel-tax hike for the renovations, the local Super Bowl committee publicly rejected a request by the NFL to exempt its executives from paying hotel taxes during their stay in South Florida for the game. The region’s rivals in Santa Clara, home to the new stadium where the San Francisco 49ers will play, granted the exemption.

South Florida has previously declined to pursue a Super Bowl scheduled the same weekend as the Miami International Boat Show. But with this bid, the region for the first time agreed to hold both events at the same time should the NFL opt to schedule Super Bowl two weeks later than usual.