"We cannot sustain the status quo. We cannot allow the situation that nobody does nothing about the current situation within the alliance..." Sdumo Dlamini, president of Cosatu, said.
The latest comments by union leaders were some of the strongest signals to date that organised labour may be ready to cut, or change, its relationship with the ANC that was forged in the struggle to end apartheid.
"We cannot sustain the status quo. We cannot allow the situation that nobody does nothing about the current situation..."
Sdumo Dlamini, president of Cosatu
The unions have set a deadline of September 2 for the government to provide a 8.6 per cent rise in salaries and a 1,000 rand ($138) monthly housing allowance.
The government is offering a seven per cent pay hike and 630 rand for housing, saying that it cannot afford the workers' demands.
Themba Maseko, the government spokesman, told Al Jazeera that the strike had raised concern and efforts were being made to resolve it.
Government services and the economy have been disrupted by the strikes, but the country's currency has suffered no major impact.
Zwelinzima Vavi, Cosatu's general secretary, said that the federation had not wanted a strike and had recommended civil servants accept the government's offer.
"We have to be loyal to our members. If they say this deal is not good enough, we have to march with them," Vavi told reporters.
"They are earning 4100 rand as a minimum wage, the lowest paid. They see a [government] minister issuing a statement about 'We must save the children' when [his] children are in a private school and he is driving a 1.3m rand Mercedes or BMW."
While the strike intensified, Zuma was in China leading a delegation of cabinet ministers and business people searching for business partnerships.
South Africa has been hit hard by the global recession, losing 900,000 jobs last year on top of already high unemployment.
The government has said it wants to devote funds to creating new jobs, not just raising the salaries of those already working.