Malcolm Green, her Labour counterpart in Glasgow, delivered a similar complaint two weeks ago.
Mrs Maginnis, a key figure in the Convention of Scottish Local Authorities, accepted that one in four schools had no boards and that most were self-selecting. But she argued that boards had been "very effective" in promoting schools and their community.
In Edinburgh, a federation was emerging to campaign on education funding.
David Hutchison, the SSBA's president, said Helen Liddell, Labour's education spokeswoman, had told him recently that she personally was "more positive" than the tenor of the party's document suggested. She had no plans to repeal school board legislation.
Mrs Maginnis declared: "I have to believe there will be a change of Government because if there is not, all of you will be running your schools. There will not be local authorities. The agenda is very clear from this Government. They do not want the strategic role of a local authority. They want schools to be small, individually based units in an agenda of splinter and fraction."
She added: "Some people say there is no difference between New Labour and the Conservatives but nothing could be further from the truth. Labour's policy document in Scotland is specifically targeted to include as many people as possible in the life of our schools and not excluding, not dividing and not creating barriers for people."
But Mrs Maginnis warned: "The problem of underoccupancy is not going to go away. It is a problem local authorities are going to have to face this year, next, the year after and into the foreseeable future.".
She chided anti-closure campaigners in Glasgow and said they were wrong to defend small urban secondary schools when places at a larger neighbourbood secondary were available. "You are actually damaging the very children you are trying to help," Mrs Maginnis said.
However, her views about small secondaries were challenged by Bill Fordyce, former director of education in Dumfries and Galloway and now an adviser to the SSBA. Mr Fordyce described her "snap statement" as "an insult to the education provided for 30-40 per cent of children in Scotland".
He pointed out that a third of secondaries would be regarded by Mrs Maginnis as too small to provide a satisfactory education.
Agreeing that councils faced "inexplicable and unacceptable" budget cuts, Mr Fordyce said: "There is a real danger the quality of education could be seriously affected next year."
In another criticism of Scottish Office policies, he advised boards to reject compulsory tests in the first two years of secondary school. These were "not worth the time, energy, effort or money which has to be expended to produce results which have little meaning in the ongoing development of the child".