Save Our Suntrap (SOS), a group representing the Friends of Suntrap, Royal Caledonian Horticultural Society, Scottish Gardeners' Forum and others, has been campaigning to preserve the 1.2ha garden as a teaching and community resource.
Chairwoman Isobel Lodge blamed the trust's financial problems for prompting the sale and added: "It has not considered our request to run the garden as the benefactors wanted."
NTS chief executive Kate Mavor claimed that the site had no national heritage significance. "Any funds from the sale would be put into a restricted fund to further the wishes of the donor, George Boyd Anderson."
The trust's director of conservation services Terry Levinthal added: "By propping up places like this we are putting the future of the trust's 35 major gardens at risk."
However, SOS has found political support for retaining the site in its current form. It has until September to come up with a plan which would not drain trust resources.
Suntrap was used as a horticultural training centre by Oatridge College until it withdraw its support after a study showed that £750,000 was required to bring facilities up to standard.