Twenty-eight female guards were unfairly dismissed by a security company because the client‚ Metrora.
BLADE Nzimande says the national health insurance system must be speeded up.
He said under the NHI, every hospital and clinic in the country would cost the same.
"We want it in a hurry," the SACP secretary-general and Higher Education Minister told about 3000 people at the SACP "Red October" launch rally at the OR Tambo Hall in Khayelitsha, Cape Town, yesterday.
Nzimande said the SACP wanted "quality health care for all". He called for an end to the private health sector's practice of leaving injured people to die if they had no money to pay the medical expenses.
Nzimande praised the ANC for its "unusual" support for the "Red October" campaign.
But the Young Communist League and Cosatu used the rally to air their grievances against the ruling party.
Young Communist League leader Buti Manamela spoke first, saying that ANC leaders who did not respect the SACP would be dealt with.
"That diarrhoea of the past, of trying to make being a communist evil, has come back to haunt us. We must deal with it in the same way we dealt with it in Polokwane," he said.
"What is shocking is that people are short-tempered when they deal with their own comrades in the alliance," Manamela said.
He said the YCL objected to the new "sweetheart" Military Services Commission, launched two weeks ago by Defence Minister Lindiwe Sisulu. Instead Manamela wanted soldiers to be allowed to join unions.
He then called on labour director-general Jimmy Manyi and Minister Membathisi Mdladlana to ban labour brokers.
He also warned against anyone in the SACP trying to topple Nzimande at the party's special congress this December.
"If there is anyone who is dreaming about replacing the SG of the SACP, just postpone your dreams," he said.
Cosatu speaker Bhekinkosi Mvovo, who is president of soldiers union Sasfu, said some in the ANC had a "hidden agenda ... to kill trade unions".
He threatened to expose generals like (Communications Minister) Siphiwe Nyanda, who he said had "started businesses instead of transforming the defence force".
But ANC deputy general secretary Thandi Modise urged the gathering to focus on wresting control of the Western Cape from the DA.