Counselling services have been set up for headteachers struggling to balance the books and at least one case of clinical depression has been reported.
The National Association of Head Teachers claims Buckinghamshire has failed to spend up to its standard spending assessment and has diverted pound;3.6 million to prop up other council services.
The union also claims that Buckinghamshire's schools are unable to benefit from Government cash being made available through the Standards Fund because the county cannot match the funding.
The financial crisis has been compounded by a change in the age of transfer to secondary school from 12 to 11 years. Primary schools have been given a transitional grant to offset loss of funding due to reduced pupil rolls, but this has been done at the expense of secondary-school budgets and does not cover all the deficit.
Muriel Pilkington, the Buckinghamshire NAHT branch treasurer, said: "The primary sector in particular is demoralised by what is happening. There are educational arguments in favour of changing the age of transfer but the actual cost has been horrendous."
David Hart, NAHT general secretary, who met 150 heads this week, said he had received reports of primary schools experiencing budget cuts of up to pound;80,000 in the coming year.
"Buckinghamshire is in danger of damaging its education service very severely indeed. The feeling among schools is one of real anger bordering on despair," he said.
In all, Buckinghamshire has had to find more than pound;15m in cuts to council services in the coming year, two-thirds of which will come from education.
David McGahey, the county's education director, disputed the job losses predicted by the NAHT but admitted that Buckinghamshire was dealing with "the most difficult budget situation we have ever faced.
"Although most schools are getting more cash than they did last year, we recognise that this is not enough and we would like to spend more. We shall be doing all we can to support headteachers through these difficult times."