Councillor Gail McIntosh said there was no appetite for a museum among ratepayers. "People are in favour of a museum so long as they don't have to pay. We need to be honest and open about that."
Councillor Bev Edlin agreed they should not string the trustees along, even though every city needed a museum.
"We need to get people working collaboratively for this city and not a pipe dream that may never come about," she said.
Deputy Mayor Kelvin Clout said there was not a great public desire for a museum and he encouraged the trust to secure external funding for a feasibility study.
Museum trust secretary John Coster was disappointed, particularly because the proposal was made by council staff. "It will take a bit longer now."
He said that without funding to get someone to do the work, there was not a lot that volunteer trustees could do. There had been no discussions about winding up. Mr Coster said if ratepayers were asked if they wanted to fund a museum then the answer would be no. But if there was a museum then people would go to it.
In another decision yesterday, the council agreed to fund part of the $200,000 cash injection requested by the Elms Foundation to keep it running. After a debate, the council decided to grant $150,000 a year for the next 10 years.