Snow removal used to be handled by the now disbanded Harbour Bridge Authority.
Transportation Minister Claude Williams said the province is considering a few options — doing the work itself, hiring a private company, or handing the responsibility over to the city of Saint John.
He's aware a decision has to come soon, he said.
"We're at the eleventh hour on that one, so we just want to assure motorists that they don't have to worry about the service, it will be provided."
Mayor Ivan Court said he's open to the city taking over the snow removal, but not at the city's expense.
"It's an obligation of the province right now," he said. "If we can assist the province, we'll do the best we can. But I have to say this — we'll have to work out some type of agreement that isn't a download on the taxpayers here in Saint John.
"If we were given money for trucks and a couple employees to do that, we'd probably consider doing that, but it can't be a downloading."
Court said the bridge requires constant clearing during the winter because of the amount of traffic going through.
The federal government agreed to turn the bridge over to the New Brunswick government, help repair the 40-year-old structure and forgive the Saint John Harbour Bridge Authority's $22 million outstanding debt.
The deal was contingent on removing the bridge's 50-cent toll.
Traffic is still restricted to two lanes where the toll booths were torn down.
The toll booths used to help slow traffic down, so the province is putting traffic-calming measures in place, including raised curbs, concrete barriers and 50 km/h speed limit signs.
That work is expected to be complete by the end of December, the minister said.
Meanwhile, repair work on the Chesley Drive on-ramp should be finished by the end of the week, and the off-ramp, by the end of the month, Williams said.
Other repairs to the bridge are expected to continue through to the fall of 2012.