Mayor Bloomberg’s plan for revamping the way trash is carted out of the city stands little chance of approval by the City Council this year unless it is revised to exclude the use of an Upper East Side facility and the administration comes clean with the plan’s exact cost.

The chairman of the council’s sanitation committee, Michael McMahon, said yesterday that the 91st Street facility that the mayor wants to use for trash was the “weak link” and the “political stumbling block” that could derail approval of the plan.

“I think that it was a mistake to not think of a better way to deal with that one portion of Manhattan’s trash,” Mr. McMahon said during a hearing in City Hall yesterday.

Mr. McMahon, who represents Staten Island, said reopening a trash-transfer facility in a residential neighborhood was not much different from the injustice his community suffered because of the Fresh Kills landfill. Until 2001, when it was shut, Fresh Kills was the dump for all of the city’s trash.

The Upper East Side marine-transfer station, not far from Gracie Mansion, also is at the district represented by the mayor’s political nemesis: the speaker of the City Council, Gifford Miller.

Mr. Miller, one of four Democrats hoping to run against Mr. Bloomberg in November, agreed with Mr. McMahon’s view and is seen as certain to block the plan if the idea of reopening of the 91st Street facility is not abandoned.

The mayor’s larger plan, which has been lauded by environmental groups, maps out a 20-year system to float trash out of the city by barge rather than transporting it by diesel trucks, as is done now. It requires reopening four waterfront transfer stations that would be used to load trash into containers and transfer containers onto barges, to be sent out of the city.

During yesterday’s hearing, several council members, including Mr. McMahon, said they could not approve a plan without concrete figures on cost. The escalating price of the plan, roughly $500 million over the next 20 years, has come under fire by some of them.

A top official at the city’s Economic Development Corporation, Kate Ascher, said the changes would run about $100 million more a year but explained that the current plan was growing more expensive by the day. Revealing more exact figures, she said, would “corrupt” negotiations with several private companies that have made offers to haul trash-filled containers. The current cost of handling trash is between $285 million and $300 million a year.

Like the mayor, Ms. Ascher said transforming the way trash is removed has to do with more than cost. It will, she said, make each borough self-sufficient in handling its waste.

“Perhaps the simplest way of thinking about this,” Ms. Ascher said, “is that the best plan is not necessarily the least expensive option.”

“The current system is not an option for going forward,” she said. “It’s not a plan, it is what we backed into when Fresh Kills was closed, and it is certainly not something that the DEC would accept.” The DEC is the state’s Department of Environmental Conservation.

A spokesman for the mayor, Jordan Barowitz, took a swipe at Mr. Miller:

“If the council insists that 91st Street not be reopened and the cheapest alternative be used, it appears that Gifford Miller prefers to send Manhattan trash to the South Bronx,” the Bloomberg aide said.

A spokesman for Mr. Miller called that a mischaracterization of the speaker’s position and said the 91st Street station would mean more truck traffic in the city.

Ms. Ascher said there is no viable alternative to the 91st Street facility in Manhattan. It would be impossible to use the West 59th Street station, as some have suggested, because it is devoted to commercial garbage, she said.

Mr. McMahon said the city was willing to “pay Starbucks prices” to a point, but needed to get “a full cup of coffee.”

One member of Mr. Miller’s Democratic majority on the council defended the plan. David Yassky of Brooklyn said the mayor was moving in the right direction.

“It’s not a perfect plan, as nothing is,” he said, “but given the options out there, I’ll tell you I cannot come up with a better one, and I don’t think there’s a better one out there.”