The board was recently placed in special measures by the Welsh Government amid concerns about management failings.
A report also condemned poor treatment of mental health patients at Glan Clwyd Hospital as "institutional abuse".
Simon Dean, deputy head of the NHS in Wales and the man appointed by the government to run the board after its chief executive Professor Trevor Purt was suspended, said last week that he had given seniors managers 100 days to start making improvements.
But Cllr Stuart Davies (pictured right), who represents Llangollen on Denbighshire County Council, predicts the initiative is “doomed to fail” and says he will demand that Wales’s First Minister Carwyn Jones considers his position when it does.
Cllr Davies has also criticised the board for failing to go ahead with an arrangement for a representative to attend the full council meeting next Tuesday to allow members to raise questions about the current situation.
He said: “I am highly disappointed that the people in charge of the Betsi are not willing to come to our meetings to answer questions about their problems. Trevor Purt had promised to attend our July meeting.
“I am particularly concerned because I wanted to seriously question them on their widely promoted 100-day turn-around plan.
“I believe this is the most idiotic idea I have heard because it will take years to turn around the deep-seated culture that is now driving the Betsi.”
He added: “They are being their usual arrogant self in not wishing to engage with councillors.
“They say on one hand they want to engage and then turn down this opportunity.
“The whole project is doomed to failure in my opinion and it is all down to the Welsh Government who are doing their usual micro-managing bit.
“I will be calling on the First Minister to consider his position when this 100-day initiative fails.”
A spokesperson for the health board said: “Professor Purt wrote out to local authorities earlier in the year, seeking an opportunity to meet with them as part of a process of public engagement to support the development of the health board’s medium term plan.
“The July date was offered by Denbighshire County Council for this.
“However, following the decision to place the health board into special measures status, the Health Minister issued clear direction that before carrying out any such discussion the health board is to carry out a widespread public listening exercise.“This exercise has now started, initially with a programme of public ‘drop in’ sessions in 15 locations across North Wales, and will continue over the coming months.
“As a result of this the health board was no longer in a position to proceed with the meeting as proposed.”