Cronin said calls for the party to "go it alone" and split from the tripartite alliance were linked to dissatisfaction and irritation with the ruling ANC.
This is also the reason many communists, and particularly young communists, are supporting former deputy president Jacob Zuma.
South Africans need to try and understand this "sea of grievance", and why it has attracted, around Zuma, a "populist and ... demagogic mobilisation".
Talk of a split is linked to a "general climate of irritation that is prevailing, which links also to the Zuma mobilisation".
"I think this 'we're going to go it alone' is linked to that irritation with the ANC. Some of the irritation is completely legitimate, in my view, but I think it's grasping at the wrong resolutions.
"But ... we're not supporting him as a candidate for presidency. We're deeply concerned about some of the things that have been said by him, or by his supporters and so forth.
"But it's no secret that many communists, and particularly lots of young communists, are supporting Zuma. Not just in some broad, general humane kind of way, but politically and presidentially. I think it's wrong.