If Graham Houston, the nationalist leader of Stirling Council, did not withdraw from his appointment "with dignity", he would call on Alex Salmond to overrule Education Secretary Fiona Hyslop.
Mr McConnell's call for Mr Houston (pictured) to quit was backed by Nicol Stephen, the former deputy education minister at the time, and by the Conservatives. They insisted the appointment of an elected politician could compromise the independence of the part-time Pounds 13,439 post of SQA chair and damage the reputation of Scottish education.
At the time of going to press, there was no indication from Mr Houston - a qualified management coach and the former Scottish director of the Work Foundation (previously the Industrial Society) - that he planned to bow to pressure to resign.
A ministerial aide insisted Mr Houston's appointment had been made in accordance with the Commissioner for Public Appointments in Scotland's Code of Practice.
Mr McConnell said part of the recovery plan for the authority in the post-crisis period was to have an independent, experienced person as SQA chair who could command cross-party support and had credibility in education. He described the appointment as "a terrible mistake", adding: "I want to believe this is just inexperience on his part and inexperience on the part of ministers in not thinking through the implications of this appointment."
He said his opposition to Mr Houston's appointment was not personal, but based on Mr Houston's position as an SNP councillor and member of the Convention of Scottish Local Authorities. "The chair of the SQA not only has to be independent but perceived as independent. As a council leader, he has an interest in his council's position and the delivery of its exams. They will at times conflict with the Government's interest and SQA delivery."
As a leading figure in Cosla, which has to negotiate the cost of delivering exams and qualifications with the SQA, there was a further potential conflict of interest, he added.