The National Association of Head Teachers is advising governors not to set deliberate deficit budgets or resign en masse, but simply to run up overdrafts.
The heads' strategy is to pin the blame for cuts on the Government by allowing schools to run out of money. They would then argue that the cuts were preventing heads and governors from carrying out their statutory responsibilities to deliver the national curriculum.
Governors should tell councils that they refuse to sack teachers and go into the red as the year progresses, heads say. Grant-maintained schools, many of which are also complaining of budget cuts, should deliver the same message to the Government.
Heads believe that the tactics will be more successful than some of the more dramatic gestures being proposed, though confrontation with the Government will take longer to arrive.
David Hart, the association's general secretary, said that, if most schools ended up with overdrafts, the debate with the Government would come to a head.
Gillian Shephard, Secretary of State for Education, says savings can be found from greater efficiency and from councils' reserves.
Mr Hart said: "It is not a debate about efficiency savings but about whether schools are being asked to deliver their responsibilities across the whole area of the curriculum with one hand tied behind their back. Governors' duty to balance the budget and deliver the curriculum are totally incompatible."
In Gloucestershire, he said, the entire £800,000 increase in funding allowed by the Government was needed just to pay for issuing statements for children with special needs.
Mr Hart accepted that the heads' strategy depended on local authorities not taking back the budgetary powers delegated to schools when schools ran into difficulties. He said: "We would be delighted if local authorities would work with us alongside governors and parents."
Schools which overspend still run the risk of having the money deducted from next year's budget.
Mrs Shephard yesterday told BBC Radio 4's Today programme that councils which had originally complained that they could not fund the teachers' pay award had now found the money.
However, Roger Hewins, chairman of the association's action committee and head of Hilliers Walk school in Hinckley, Leicestershire, said that, although the award would be funded at his school, it faced a £30,000 deficit. Last year the cut was £15,000.