EAST RUTHERFORD, N.J.—Developers and elected officials ratcheted up demands on Wednesday for a statewide referendum to expand gambling to the northern part of the state, a display of public pressure timed to coincide with the unveiling of a proposed $1 billion Hard Rock Casino in the Meadowlands.

The casino would feature 5,000 slot machines and 200 tables for gambling, along with a giant guitar that operators said could be visible from Manhattan. It would be located west of New York City, adjacent to MetLife Stadium, where the New York Giants and New York Jets play.

“We are not looking to build slots in a box,” said Jim Allen, chairman of Hard Rock International, while releasing the proposal at Meadowlands Racetrack. “We believe this will compete with anything in the world.”

Operators projected the casino could initially generate at least $400 million in annual tax revenue and create 5,000 jobs. Its doors could open by next summer or early 2017, they said.

On stage for the slick presentation were half a dozen state Democrats, who pledged to push forward with an amendment to the state constitution that would allow an expansion of gambling in New Jersey for the first time in nearly four decades.

Gambling in the state is currently limited to Atlantic City, but a group of North Jersey lawmakers introduced a resolution on Monday to ask voters whether it should be expanded to Bergen, Essex and Hudson counties. Up to three casinos would be allowed under the proposal.

The group of Assembly representatives didn’t initially provide a timetable for the amendment, but backers Wednesday gave a full-throated endorsement to putting it on the ballot this November.

“We have to put this on the ballot this November and get it done now,” said Sen. Ray Lesniak, a Union County Democrat.

Assembly Speaker Vincent Prieto, a Hudson County Democrat, said conversations would start immediately about whether to put it on the ballot this year. “We need to do this right now,” he said.

Sen. Paul Sarlo, a Bergen County Democrat, said “I would like to see this on the ballot immediately.”

In March, a Fairleigh Dickinson University PublicMind poll found that 57% of New Jersey adults opposed expanding gambling beyond Atlantic City, while 36% favored it.

The gambling push has come to a head as officials face an Aug. 3 deadline to approve the question to be placed on the ballot in time for the Nov. 3 election.

The coalescing of North Jersey lawmakers behind a vote this year puts additional pressure on Senate President Stephen Sweeney, a South Jersey lawmaker. Mr. Sweeney, a Democrat, has said he supports North Jersey gambling but wants to see the question go before voters in 2016.

South Jersey lawmakers have criticized the expansion, saying it would take revenue from an already struggling Atlantic City. Competition from casinos in New York and Pennsylvania has badly eroded the seaside resort’s previous monopoly on gambling in the region.

A spokesman for Mr. Sweeney declined to comment on Wednesday. Gov. Chris Christie has said he supports putting the question before voters as soon as possible and would publicly back its passage.