The ANC top-six officials, including President Cyril Ramaphosa, will meet on Friday to discuss changes to the cabinet, according to three people who asked not to be identified because they aren't authorised to speak publicly on the matter.
The situation has forced him to carry on for a while with the ministers he inherited from his predecessor, Jacob Zuma.
Gigaba said poor households would be cushioned against the Value-Added Tax rate rise through a zero-rating of basic food items such as maize meal and beans, and welfare payments increases.
He said Monday's debate was conducted in a respectful manner and that it engaged with the issues that most directly affect the people of South Africa. "If you live on an extremely tight budget and have to count every rand you have, it will affect what you can buy".
The government of Africa's most industrialised country has to plug a revenue hole in its budget and fix its economy after nine years of mismanagement under the scandal-plagued Jacob Zuma.
John Meyer, mining analyst and founder of the London based nomad and broker, SP Angel, says that his experience of the event that he attended this year, was that it was "jam packed" with both companies and investors that were interested in getting together to fund projects.
The budget´s proposals to generate an additional 36 billion rand in tax revenue will be essential to fund free university education for students from low-income families - a policy abruptly announced by Zuma on the eve of his departure from the ANC presidency previous year.
Ramaphosa could also appoint Nhlanhla Nene, another finance minister that Zuma fired and replaced with a little-known lawmaker in 2015, to the cabinet, the people said.
Ramaphosa was elected as South Africa's fifth president the following day and was duly sworn in later the same day.
New President Cyril Ramaphosa should take action within 14 days against Brown, whose department oversees enterprises including Eskom, said Busisiwe Mkhwebane.
"We will accelerate our land redistribution programme not only to redress a grave historical injustice, but also to bring more producers into the agricultural sector and to make more land available for cultivation", Ramaphosa said. "There is positive sentiment".
Mr Ramaphosa was the only candidate nominated for election after two opposition parties said they would not participate.