Paul Bennet, of Canterbury Archaeological Trust, explains some of the Roman Museum's exhibits
More than 2,000 people have signed an online petition and joined Facebook groups against the proposed closure of three Kent landmarks.
Canterbury City Council (CCC) is considering the future of the Roman Museum, Westgate Towers and Herne Bay Museum, to save £3m over two years.
Campaigner, Ida Linfield said: "The[Roman Museum] is part of history. It was a town of huge importance."
The final decision will be made at a full council meeting on 18 February.
Paul Bennet from Canterbury Archaeological Trust said: "They're (CCC) trying to save a huge amount of money by getting rid of our heritage.
"I'm really sad about the whole situation, this is the only place where you can go beneath the streets of Canterbury and see a Roman pavement.
"The pavement was so important they showed it to the King and Queen when they visited in 1946."
More than 2000 people have signed the "Save Canterbury's Museums Petition".
The council said the proposals were being considered because of an expected shortfall in its government grant.
Westgate Hall is also being considered for closure.
Council leader John Gilbey said: "Westgate Hall has been a drain on the council for years.
"It is an old drill hall which is costing over £100,000 a year and will cost £1m to bring it up to scratch, so it's almost certainly going to close."