Former Cosatu general secretary Zwelinzima Vavi and EFF leader Julius Malema are plotting to overthr.
Marching to the township near Zuma's homestead on Saturday, the SACP brought the rural town to a standstill with more than 10,000 members of the SACP and its alliance partners swarming to the area.
While both the Department of Public Works and the public protector are already investigating the costs and contracts for the R250-million improvements, the SACP believes this is not enough.
The party wants a forensic investigation that will look into the costs of renovations and whether there has been inflation of prices and who was responsible and to whose financial benefit.
They also demanded a probe to find out if there existed an organised siphoning off of taxpayers' money through political networking targeting the government property and infrastructure budget through the department of Public Works.
An emotional Zuma said in Parliament on Thursday that he was paying off a bond on the Nkandla homestead himself, but City Press yesterday reported no such bond existed.
Yesterday presidential spokesman Mac Maharaj said he was not privy to any information regarding the bond.
The president's homestead is constructed on the land owned by the Ingonyama Trust, headed by King Goodwill Zwelithini.
On Saturday, SACP provincial secretary Themba Mthembu said their march on Nkandla was meant to highlight serious challenges faced by rural communities with a high backlog in development.