Obama, on a three-nation tour of Africa, was due to arrive in South Africa on Friday with White House officials saying they will defer to Mandela's family on whether the first African-American president of the United States will visit South Africa's first black president.
Mandela (94) is fighting a lung infection that has left him in a critical condition and in hospital for nearly three weeks.
His fourth hospitalisation in six months has focused attention in South Africa and globally on the faltering health of the Nobel Peace Prize laureate, who is admired as a symbol of resistance against injustice and of racial reconciliation.
President Jacob Zuma has said Mandela's condition improved over Wednesday night but he remained critical.
About 200 trade unionists, student activists and South African Communist Party members gathered in the capital Pretoria to protest Obama's visit this weekend, calling his foreign policy "arrogant, selfish and oppressive".
"We had expectations of America's first black president. Knowing Africa's history, we expected more," said Khomotso Makola, a 19-year-old law student.
"He has come as a disappointment, I think Mandela too would be disappointed and feel let down," Makola said.
South African critics of Obama have focused in particular on his support for US drone strikes overseas, which they say have killed hundreds of innocent civilians, and his failure to deliver on a pledge to close the US military detention centre at Guantanamo Bay in Cuba housing terrorism suspects.
Two great men
A few blocks away at the Pretoria heart hospital where Mandela is being cared for, well-wishers paying tribute to the legendary retired statesperson had words of praise for Obama, who met Mandela in 2005 when he was still a US senator.
Nigerian painter Sanusi Olatunji (31) had brought portraits of both Mandela and Obama to the wall of the hospital, where flowers, tribute notes and gifts for Madiba, as Mandela is affectionately known, have been piling up.
"These are the two great men of my lifetime," he said. "To me, Mandela is a prophet who brought peace and opportunity. He made it possible for a black man like me to live in a country that was only for whites."
During his weekend trip to Johannesburg, Pretoria and Cape Town, Obama is scheduled to visit Robben Island, the former penal colony where Mandela passed 18 years of the 27 years he spent in apartheid prisons.
Visit to Africa
Starting off his Africa trip in Senegal on Wednesday, Obama praised Mandela as "a personal hero".
"If and when he passes from this place, one thing I think we'll all know is that his legacy is one that will linger on throughout the ages," he told reporters in Dakar.
Obama, who has been in office since 2009, is making his first substantial visit to Africa following a short trip to Ghana at the beginning of his first term.
South Africans held prayer meetings and vigils outside the Pretoria hospital and at Mandela's former Soweto home through Thursday night.
But as his health has deteriorated this year, there is a growing realisation among South Africa's 53-million people that the man who forged their multi-racial "Rainbow Nation" from the ashes of apartheid will not be with them forever. – Reuters