They are not the only ones though, as several civil society organisations under the banner of Future SA have written a letter to ANC president Cyril Ramaphosa, calling on the party to put the country first by ensuring that Zuma doesn't deliver this week's address. This after Zuma failed to heed appeals from his comrades on Monday that he must do the honourable thing and resign.
The national executive committee is the ANC's highest decision-making body and can "recall" Zuma from the post of president - though he could refuse to comply. Ms Mbete did not give a new date for the speech.
While the country was digesting that shock announcement, Zuma held a meeting with Ramaphosa where the ANC says the two agreed on the postponement and discussed other issues. Opposition parties and some in the ANC want him to go before his State of the Nation address to parliament, scheduled for Thursday.
Since Mr Ramaphosa beat Nkosazana Dlamini-Zuma, Mr Zuma's favoured successor and ex-wife, in the December vote for the party leadership, the president's fortunes have waned.
The president has been enmeshed in a series of scandals but denies wrongdoing. Ramaphosa will be the ANC's presumptive presidential candidate when the nation votes next year.
"President Zuma has abused the trust of South Africans", said Sello Hatang, the foundation's CEO.
The ANC had earlier heavily flagged Wednesday's scheduled meeting of its leaders by saying they would decide a "matter of serious concern". Zuma has survived nine votes of no-confidence, but his party has increasingly split over his unpopularity, and another no-confidence motion is scheduled for February 22.
Dlamini Zuma was perceived to have been Zuma's preferred candidate at the ANC's conference at the Nasrec Expo Centre previous year, and there are some who believe she would help protect him from prosecution on the corruption charges set to be reinstituted against him. The embattled president also told the ANC leadership pushing him out would create serious divisions within the party because "people still loved him".
Malema said Zuma told the new party leaders that he has performed his duties, and done everything he was requested to do as state president.
This move was seen as a major victory for the opposition who had demanded that Zuma not deliver the address.
BLF members had meant to protest outside the ANC headquarters and hand over a memorandum demanding that beleaguered President Jacob Zuma serve out his term, which ends next year. "Not even lunatics do what these ANC members are doing, they have lost what we call uBuntu (humanity)", the NFP said.
Zuma's almost two terms in office have been blighted by hundreds of corruption allegations, but he has so far managed to dodge prosecution.