Party leaders had failed to resolve the deadlock in hastily scheduled meetings this week. Another meeting — this time of the party’s highest decision-making body, the 86-member national executive committee — was scheduled, again hastily, for Wednesday.
In a news conference on Tuesday, Jessie Duarte, the deputy secretary general and one of the party’s “top six leaders,” said that Mr. Zuma’s future would be discussed by the executive committee on Wednesday.
“We don’t know the outcome,” said Ms. Duarte, a longtime Zuma ally. Referring to the committee, she added: “Let the N.E.C. provide us with a decision. Up to this point, there has been no decision.”
Mr. Zuma, a survivor who has defied political gravity for years, had told supporters that it was his right to give the speech, though on Tuesday his office said that he had agreed to the postponement. According to the news media, he has given no indication of stepping down, saying that the “people still love him.”
In South Africa, the president is appointed by Parliament, which is dominated by the A.N.C. If the party’s executive committee turns against Mr. Zuma, he would most likely resign, or face a humiliating fate in Parliament.
The annual address has produced dramatic political theater in recent years. While A.N.C. lawmakers have visibly supported Mr. Zuma during past speeches, opposition lawmakers have used what amounts to the president’s most important speech of the year to humiliate him.
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The Economic Freedom Fighters, the nation’s second largest opposition party, whose members dress in red overalls, have delayed the start of Mr. Zuma’s previous speeches, heckled him and demanded his resignation before walking out en masse. Should Mr. Zuma deliver the address, the Economic Freedom Fighters have promised similar actions.
But an address by Mr. Zuma would leave some A.N.C. lawmakers in a difficult situation — whether to visibly support him, adopt a critical pose, remain neutral or even boycott the address.
The Economic Freedom Fighters and other opposition parties are also pushing for Mr. Zuma’s resignation. A motion of no-confidence called by the Economic Freedom Fighters has been scheduled for a vote in Parliament on Feb. 22.
That, too, would put A.N.C. lawmakers critical of Mr. Zuma in a difficult situation. The party has helped Mr. Zuma survive previous opposition-led votes of no confidence. While many members of the governing party want Mr. Zuma to step down, some have said that they do not want the opposition to lead the effort.
Mr. Ramaphosa, who has been nudging Mr. Zuma to resign without deepening the party split, has said that Mr. Zuma should not be humiliated. His supporters say that reflects Mr. Ramaphosa’s skillful negotiating style and his view of the big picture.
But others interpret Mr. Ramaphosa’s attitude as a sign of weakness. Julius Malema, the leader of the Economic Freedom Fighters, said in a television interview that Mr. Ramaphosa was “a coward” and that the A.N.C. was paralyzed.