NCA official, Blessing Vava said it was folly to assume that since the three parties had assented to the draft, the public would also accept it.
"I do not think everyone is endorsing it. Only leaders of political parties are happy" he said. "If you look at our critiques of the draft, you will realise that we are raising fundamental issues."
Vava said the NCA was mobilising its supporters and partners to campaign against the draft, which he described as a negotiated settlement, rather than people- driven.
NCA leader, Lovemore Madhuku has also strongly rejected the draft, saying he was opposing it on matters of principle. He told a meeting in South Africa last week that all voices must be heard to promote plurality.
"A yes campaign by all promotes a wrong precedent," he said, adding that it was better to invest in a proper process. "The issue is not about whether 'no' vote wins, it is about principle to allow all voices and promote plurality."
But supporters of the draft constitution say this will be Zimbabwe's real chance of entrenching constitutionalism, where the authority of the government is derived from the people.
Constitutionalism entails institutionalised mechanisms of power control for the protection of the interests and liberties of all citizens, including those that may be in the minority.
"This process gives Zimbabweans an opportunity to decide their fate," MDC secretary general, Priscilla Misihairabwi-Mushonga told an Open Society Initiative of Southern Africa meeting on Friday.