In an unprecedented move to demonstrate the depth of their feelings, they are refusing to talk to the Executive - or, as they put it, "we should not engage constructively with the consultation process at this stage".
The Executive's plans are set out out in Ensuring Improvement in our Schools, on which the consultation ends today (Friday).
In one of its most cutting statements of recent years, the leadership of the Convention of Scottish Local Authorities which meets in Edinburgh today, complains that the move is part of a trend which poses "a fundamental threat to local democracy".
The new powers "are being driven by a political agenda that promotes the view that local government cannot be trusted to provide the quality of services expected by the public and therefore the Executive should have the power to intervene directly", the statement declares.
Peter Peacock, Education Minister, has said repeatedly that extra powers are needed only as a last resort but are necessary to close a loophole in existing legislation.
But Cosla retorts: "There is no evidence that there are so-called failing local authority schools that require national intervention. There is no evidence that any local authorities or local authority schools would not respond in a proactive way to redress major problems identified in HMI reports."
The authorities also suggest that the Executive's "pre-emptive and unnecessary" proposals go against the grain of the conclusions of the national education debate which promised to introduce greater flexibility for schools and authorities, review legislation to reduce bureaucracy and devolve more power to headteachers.
The convention points out that the 2003 Local Government Scotland Act already allows ministers to intervene in all council services. Extra powers would go against the principle of "best value".