Education authorities have blamed teachers' pay increases for their failure to maintain numbers and reduce class sizes.
Isabel Hutton, education spokes-person for the Convention of Scottish Local Authorities, said it would be "economic suicide" for councils to maintain teacher numbers while school rolls were falling, salaries were rising and record demands were being placed on children's services.
She was reacting to the Scottish Government's threat to wrest education from local authority control because of councils' lack of progress on its flagship class-sizes policy, and an embarrassing fall in teacher numbers for the second year running.
It was "no coincidence" teacher numbers fell by 2.5 per cent, which was "exactly the salary increase in the current year of the teachers' pay deal", Ms Hutton continued.
She described Government accusations that councils had made savings from reducing teacher numbers, or redirected those resources elsewhere as "disappointing and ill-informed". This was a surprisingly robust intervention from an SNP councillor who is a close political ally of former Education Secretary Fiona Hyslop.
She warned that council finances would get worse before they got better and added: "Next year is likely to be the last when local government expenditure on education will rise."
The Scottish Government, however, has called an unprecedented meeting between the Cabinet and Cosla leaders at which "everything will be on the table", including removing education from council control. The agenda will not alter with this week's change of ministers, a Government spokesman confirmed.
Last week, Ms Hyslop, in almost her last act as Education Secretary, said the Government was keeping an open mind. Alternatives to local authority control over education might mean placing more power in the hands of schools or controlling education from the centre. She also pointed out, however, the two were not mutually exclusive.
And one headteacher, who has experience of working in schools within and outside council control, argued that schools could deliver Government education policy more effectively than local authorities. Schools were keen to please inspectors, he argued, and would therefore cut class sizes if that was one of the criteria upon which they would be judged.
Schools run by trusts, as suggested by East Lothian Council, would also be able to make decisions more quickly and cheaply, he felt.
The downside, he admitted, was that a headteacher could become an "uncontrolled dictator".
Ms Hyslop acted quickly in response to two sets of official statistics issued at the end of last week: just 13 per cent of P1-3 pupils are in classes of 18 or fewer for the second year running, and the total number of teachers in Scotland has fallen by 1,348 since 2008 in spite of the SNP manifesto pledge in 2007 to maintain teacher numbers.
The lack of progress on class-size reduction was described as "unacceptable" by Ms Hyslop, speaking at the Association of Directors of Education in Scotland annual conference in Cumbernauld last week.
"We now have to find a new way forward to ensure class-size reductions in P1 to P3 are delivered in all of Scotland's councils," she said.
"Everything will be on the table and we will keep an open mind. We will discuss how best to establish where the estimated pound;110 million that could have been spent on teachers' salaries has been spent, what help can be offered to individual councils facing specific difficulties and whether the Scottish Government needs to examine alternatives to the current system of local government delivery of education policy."
Cosla president Pat Watters said there was not a councillor alive who thought maintaining teacher numbers was the right thing to do.
"Local councils and local people treasure education as their own and Cosla and local government would do everything in their power, and take every step, to make sure it remained that way," he said.
The "hidden threats" in Ms Hyslop's announcement were not in the spirit of the concordat between central and local government, he added.
Councils like East Ayrshire, Angus, Midlothian and South Ayrshire, run by a variety of political coalitions, were making "real progress" on reducing class sizes to 18 in early primary, Fiona Hyslop said.
Glasgow City Council, however, was an example of an authority that was "deliberately refusing" to reduce class sizes, she said. It was responsible for one-quarter of the total fall in teacher numbers, which the former Education Secretary described as "deplorable".
SNP-run East Ayrshire Council had put 30 additional teachers into early primary by maintaining teacher numbers in the face of falling rolls and redirecting teachers from pre-school into the early years of primary.
Now 41 per cent of P1-3 classes in East Ayrshire contained 18 pupils or fewer, up from 7 per cent last year. This is way beyond progress in any of the other non-rural authorities; of those, West Lothian is the next best performer but with only 24.9 per cent. By contrast, Renfrewshire and Dundee have managed to hit the target in only 5 per cent of P1-3 classes.
Graham Short, East Ayrshire's director of educational and social services, said the combination of falling rolls and the new early years service had allowed the council to invest an additional pound;600,000 in early primary. "We have yet to evaluate the new approach but the feedback from headteachers and parents is that they welcome this development," he said.