The calls for her removal by the ANC’s top leadership come amid mounting evidence suggesting she misrepresented her qualifications.
Tshabalala is now accused of pitting Luthuli House against the government and Communications Minister Faith Muthambi by “trying to create a distance” between the ANC and government, according to one senior party leader.
While the ANC can’t do much about the matter, it is hoping Muthambi “will do the right thing” and suspend her if she refuses to resign.
Tshabalala met Muthambi on Wednesday in what was possibly a discussion about her future and her decision to stay on.
Commenting on Wednesday, Tshabalala said: “I have no intentions to leave”.
“I have not been found guilty of anything so I don’t have intentions to leave, this is just the beginning of my contract.”
A senior leader of the ANC said what was of great concern to the party was that “she is not playing honestly”.
After the ANC’s national executive committee meeting last month, Tshabalala was asked to fall on her sword.
ANC insiders in the party’s national executive committee and in Parliament said last week she would be asked to resign.
Tshabalala said on her CV that she had a BCom from Unisa and a diploma in labour relations.
The university said it had no record of these.
On October 14, she is to appear before the communications committee to answer allegations that she misled Parliament about her qualifications.
Tshabalala said the matter was sub judice and before Parliament, so she could not discuss anything in detail in the media.
“As for informing my shareholder what steps I’m taking, I’m meeting with (Muthambi) today. I can’t disclose details of that (meeting), it’s a confidential matter.
“The whole issue of my credentials is my matter with my shareholder and then obviously her reporting to Parliament about it.
“I’m following that route and I can’t discuss it publicly,” said Tshabalala.
She would “not entertain” ANC secretary-general Gwede Mantashe and the party’s calls for her to resign.
“I don’t report to Mantashe, I report to Minister Muthambi,” said Tshabalala.
A senior ANC leader said “whether she (Tshabalala) likes it or not the ANC has every right to be concerned”.
“She cannot bully us into silence.”
Public Enterprises Minister Lynne Brown has written to Tshabalala to get clarity.
After the reports came to light, Brown sent Tshabalala and Transnet board chair Mafika Mkwanazi a letter asking them to respond to the allegations.
“I’m told she has responded, but through a lawyer,” said Brown.
Should Tshabalala provide proof of her qualifications, “everything goes back to normal”.
“If not then she must go. It’s that simple.”
In another development, the SABC’s annual report, tabled in Parliament this week, shows she was paid nearly R1 million for the 2013/14 financial year, almost double the sum paid to her predecessor.
She was paid R936 000 for chairing 34 board meetings and attending 36 board committee meetings.
Her predecessor, Ben Ngubane, was paid R521 000 for the previous year.
DA communications spokesman Gavin Davis said if it was found Tshabalala had misrepresented her qualifications, she might be liable – under the SABC’s fraud and corruption policy, as stated in its annual report – to pay back the R936 000 and any other money paid to her.