In a joint statement issued on Friday, Labor senator Malarndirri McCarthy and member for Solomon Luke Gosling called on Indigenous Affairs Minister Nigel Scullion to stop Larrakia Nation's imminent closure.
The organisation, which runs night patrol, aged care, ranger and homelessness services throughout Darwin, went into special administration in June amid internal strife.
This was mainly due to an inability to recoup the cost of helping people travel back to remote communities under its Return To Country program.
Ms McCarthy and Mr Gosling said the organisation has been working hard to resolve its financial issues since then by reducing debts and strengthening management processes.
"But issues with Centrelink's Centrepay system, that clients of the Return to Country program use to pay their fares in instalments, has left a nearly $500,000 hole that may force the organisation to close," they said.
Labor said more than 60 workers could lose their jobs if the debt isn't repaid by the December deadline.
They said Mr Scullion has ignored requests for consultation and called on him to ensure Centrelink recovers the money owed to Larrakia Nation.
"It's disgraceful the minister will not meet to discuss the future of an Indigenous organisation that operates in his backyard," they said.
The night patrol service, which takes people who have been drinking to a shelter to sober up, worked with 10,000 clients last year with demand continuing to grow, Ms McCarthy and Mr Gosling said.
Mr Scullion has been contacted for comment.