Former Cosatu general secretary Zwelinzima Vavi and EFF leader Julius Malema are plotting to overthr.
“I am happy Madiba is back home, I wish him a happy new year and he must push for more years,” said one man, before pulling off.
A minibus carrying German tourists stopped at Mandela’s home.
“ I wish him best and well; we are happy to see his house,” said one passenger.
Mandela was discharged on Wednesday, after he was flown to a Pretoria hospital from his home in Qunu in the Eastern Cape on December 8.
He was diagnosed with a lung infection and also underwent gallstone surgery.
The elderly statesman has a history of lung problems, having suffered from tuberculosis towards the end of his 27-years spent in prison.
Four policemen were seen outside the gate controlling access to the house.
Two black cars with military number plates parked a few metres from the gate.
International and local journalists are camped outside Mandela’s house.
Television cameras are focused on the entrance of the house, while photographers took pictures of cars and people passing near the house.
Painted rocks with birthday messages still decorate flower beds outside his home. Mandela turned 94 on July 18.
“Mandela we love you,” read one stone, painted in white.
A yellow one read: “Nelson Mandela, if we [could] have our way we would keep you for ever.” Mpho Xolo wrote “Lots of love from South Africans.” The presidency said on Wednesday that Mandela would be under home-based care at his Johannesburg home until he recovers fully.
He spent Christmas Day in hospital. It was his longest stay in hospital since he was released from prison over two decades ago.