The ANC could "recall" Zuma, which would pressure him to resign before his term ends next year.
Zuma broke his silence Wednesday in a live interview with state broadcaster SABC as the nation awaited word on whether he would obey a ruling party order to leave office.
However, with the ruling African National Congress (ANC) backing an opposition-led no-confidence motion likely to be heard on Thursday, Zuma appears to have run out of road after nine years in office dogged by scandal and economic stagnation.
The "Zexit" (Zuma exit) saga has intensified as opposition parties and the ANC try to get Zuma recalled or convince him to resign. Another senior party official suggested that Zuma would be unwise to flout the edict of the party, which is eager to recover from internal disarray ahead of 2019 elections.
Magashule said the party did not give Zuma a deadline to tender his resignation, but said they expected a quick turnaround.
A lawyer for the Gupta family said he could not comment on the raid because he had yet to see the search warrant.
The next step for the ANC in the event of defiance by Zuma would be for the ANC to use the constitutionally mandated parliamentary process of a vote of no confidence, Absa Capital economists, Miyelani Maluleke and Peter Worthington, stated.
As the deadlock escalated, the party on Tuesday "recalled" Zuma from his post after days of failed closed-door negotiations with Ramaphosa.
His tenure has been marred by allegations of corruption and personal scandals.
The country's top court also ruled in 2016 that the President had violated the constitution when he used state funds to pay for multi-million dollar upgrades to his private home.
Another committee member told AFP that Zuma's response was "hogwash" and that the president had asked for three more months in office.
Many graft allegations against him have centred on the wealthy Gupta family, who are accused of unfairly obtaining lucrative government contracts and even being able to choose ministerial appointments.
On Wednesday morning, the country's anti-corruption task force, The Hawks, raided the Saxonwold compound of the Gupta family - three brothers whose business affairs have become inextricably bound with those of Mr Zuma.
A judicial commission is about to start a probe of those allegations. The president also faces almost 800 corruption allegations stemming from an arms deal during the 1990s.