As the City Council quietly juggled a hot potato tossed by a former colleague, lawmakers on Beacon Hill threw another overheated spud its way.

The sudden resignation of Dorchester City Councillor Maureen Feeney set in motion widespread speculation that she is headed for the higher-paying job of city clerk. The council has the power to vote her into the cushy gig and could do so before the end of the year— if they choose to dislodge the current clerk, Rosaria Salerno.

Last week, State House lawmakers handed the city councillors another power, which may cause even more heartburn for the 13-member body. Tucked into the final version of the casino bill lawmakers sent to Gov. Deval Patrick last week was a provision giving the City Council the authority to set up a city-wide referendum on a gaming facility.

Another option is the one preferred by Mayor Thomas Menino and some of East Boston’s elected officials: Limiting the decision to voters in the single ward that would host a proposed casino. Menino told Channel 5 that he supports the position of state Sen. Anthony Petruccelli, a Democrat from East Boston, where a casino could be sited on the grounds of the Suffolk Downs race track. Menino and Petruccelli argue that East Boston, not the entire city, should have a say in whether or not a casino goes up within its borders.

The casino bill authorizes three Bay State casinos and a slot parlor. The Suffolk Downs horse track, located in East Boston and between Revere and Winthrop, is expected to make a casino application. Locally known as Eastie, the neighborhood was once a shipbuilding center and is now home to Logan International Airport and more than 40,500 people.

“I don’t believe in referendums but if the local elected official wants it for his section of the city, I’d support that,” Menino said on the weekly political chat show “On the Record.” The mayor is a top backer of casinos. Pressed by Channel 5 reporter Janet Wu, Menino said, “Government by referendum doesn’t work. Because one side will spend a lot of money to try to defeat it because they have an agenda…Let the people who it’s really affected make that decision.”

This debate could put some city councillors in an awkward position, especially those whose constituencies include a mix of progressives and union members. Unions have long pushed for casinos and have flooded the halls of the State House, pointing to the potential windfall of construction jobs that would be generated. Progressives call casinos a regressive tax on the poor, and state Sen. Sonia Chang-Diaz, a Jamaica Plain Democrat, has pressed for a city-wide vote through an amendment the Senate ended up voting down. She has pointed to a memo from Secretary of State William Galvin, the commonwealth’s elections chief and a Brighton Democrat, who said a ward-only vote could leave a city open to legal challenges.

Some city councillors and their aides — including Tito Jackson, who represents Roxbury and a part of Dorchester, and staffers with City Councillors At-Large Ayanna Pressley and Stephen Murphy — said they were still reviewing and soliciting input on the casino legislation, which landed on the governor’s desk last week.

Sal LaMattina, a district councillor who represents East Boston and parts of Charlestown and the North End, said he prefers to keep the referendum limited to Eastie. Someone in Readville, West Roxbury, or Jamaica Plain should not determine whether a casino is sited in East Boston, he said.

Would East Boston approve a casino?

“I don’t know, to be honest with you,” said LaMattina, who has supported slots at Suffolk Downs. There are pros and cons, he added, and it’s up to Suffolk Downs to reach out and listen to the concerns of the neighborhood.

If East Boston opposes a casino, he’ll oppose it as well, LaMattina said, and vice versa. But right now his position is to work with the neighborhood to see what kind of improvements to transportation and infrastructure they would receive should a casino get built, he said.

His colleague, Mark Ciommo, a casino supporter who represents Allston-Brighton, acknowledged that the presence of a casino would affect the entire city, as well as surrounding communities. But he would also give deference to the neighborhood hosting the casino.

“I want to give the folks who are going to be mostly impacted as much input into this process as possible and I don’t know if they get that by letting folks from the entire city vote on it,” he said.

A few councillors believe the referendum should include the whole city. Matt O’Malley represents Jamaica Plain and West Roxbury. He would likely vote for a casino, he said, but if there is a referendum, “it would make sense to make it city-wide.”

“The casino is going to affect the entire city,” said Frank Baker, who will be sworn in as the district councillor for most of Dorchester in January, succeeding Feeney.

Baker is a casino supporter, with deep union roots.

"I don’t think a referendum in East Boston would block it,” he said. “Opening it up to the city would ensure that people’s concerns are met.”

Other members of the City Council were not immediately available for comment.

EDITOR’S NOTE: Material from State House News Service was used in this report. Check out updates to Boston’s political scene at The Lit Drop, located at dotnews.com/litdrop. Follow us on Twitter: @LitDrop and @gintautasd.