The move - which comes amid financial woes at universities including Otago - is part of a national reorganisation of Te Pukenga, the newly merged mega national institute comprising 24 institutes including polytechnics.
Nationally, 400 redundancies - largely in management and support roles - are threatened, out of 10,000 Te Pukenga staff.
Te Pukenga refused to say how many staff were affected at Otago Polytechnic or SIT, describing this as unavailable "detail".
Otago Polytechnic had more than 900 staff and SIT has 400.
Sources said about 5% of roles may be affected.
Staff at risk were contacted individually to be told the bad news and Te Pukenga management addressed an online video meeting for all staff yesterday.
Tertiary Education Union organiser for Otago and Southland Daniel Benson-Guiu said staff were overwhelmed.
"There was a huge amount of information given in one fell swoop," he said.
"People have been in tears, leaving their desks, and there is palpable tension that has been building for months.
"Staff were already under additional pressure due to staff vacancies not filled and overwork."
Staff were told a consultation document would be circulated yesterday afternoon and decisions would be made in August.
However, at the end of business yesterday staff had not received the document.
"This was D-day - but we are left not knowing what it all means," one staff member said.
Another described the delay as "crazy stressful for anyone whose job is on the line".
Addressing the online meeting, Te Pukenga chief executive Peter Winder described the reorganisation as a "very big and complicated change proposal", and said the anticipated redundancies were "not something we take lightly".
"We acknowledge that for many this will be a quite stressful time when they will have received some quite confronting information."
Most staff were expected to experience only minor changes - a "lift and shift" in who they reported to, Mr Winder said.
About 550 new and exciting roles were also expected as part of the proposal, he said.
There was an expectation some staff in discontinued roles would be able to move to new roles.
The threatened roles were partly due to the creation of national departments for various support functions, such as business development and marketing.
Autonomous departments previously undertaking these functions within institutes were expected to be affected.
It is understood staff to be employed within the new national departments would be sought from across New Zealand’s polytechnics.
The positions of existing executive directors of institutes, currently leading "transitional leadership teams", were among the threatened roles, sources said.
Otago Polytechnic executive director Chris Williamson and SIT executive director Daryl Haggerty were both unavailable for comment.
However, in a message to staff, Mr Williamson described the timing of the consultation as "challenging, as the semester draws to a close".
The current financial health of New Zealand’s polytechnics is unknown and Te Pukenga’s financial accounts for 2023 are overdue.
The Office of the Controller and Auditor-general told the ODT it was "working closely with Te Pukenga to finish it as soon as possible".
This week it was revealed Otago Polytechnic enrolments were down by 10%, and SIT had also announced a 5% drop in domestic enrolments.
In a statement yesterday, Mr Winder admitted Te Pukenga had faced "considerable financial headwinds" but the restructure would "remove expensive duplication and inefficiencies".
Invercargill MP Penny Simmonds, a previous head of SIT, described the announcement as "absolutely disgraceful" and said she had been "pushing" for Te Pukenga’s financial report.
Southland Business Chamber chief executive Sheree Carey called for the "preserving of the autonomy and unique character of our local institutions".
