As part of its Phase 2 cuts proposals RCT Council are looking at closing Cynon Valley Museum, cutting the service at the Rhondda Heritage Park and withdrawing its SLA (Service Level Agreement) from Pontypridd Museum.
The consultation ended last month but as yet the Cabinet has not met to decide on the final outcome.
Welsh Liberal Democrat Councillor Mike Powell says that the Council has to take a closer look at where these fit in the overall picture.
"The evidence put forward to back the proposals was sketchy to say the least particularly in relation to Pontypridd Museum where there was little detail as to what the SLA actually provides and no mention of how many visitors there are to the Museum.
"The Council have failed to adequately market any of these attractions, but in the case of Pontypridd its own performance report for the year clearly states that 'Pontypridd Museum attendances continue to be affected by town centre regeneration.'
"Now this is a strange statement in itself given that they are so keen to brag about what a success the regeneration has, in their view, been. If it has indeed been money well spent as they claim then why would it adversely affect the Museum?
"The SLA is for a mere £36,000 a year, a drop in the ocean in the context of the cultural service budget, and certainly nothing in view of the amount that has been spent on Pontypridd. It is surely unfair to remove funding from this centre when the Council's own mishandling of the regeneration of the town is the cause of its downturn."