Mr Christie, treasurer of the Association of Directors of Education, said such a plan was "one step away from ring-fencing money for the education service".
Michael Forsyth, facing a storm of protest from hundreds of Borders parents as he arrived for the Scottish Grand Committee in Selkirk on Monday, accused local opponents of playing politics with children's education and revealed he would consider a specific grant scheme if councils cut tuition.
Borders faces education cuts of Pounds 3.8 million - 8 per cent of the budget - and may have to close seven primaries, lay off staff and axe visiting specialists in music, art and physical education. Instrumental instruction costs Pounds 300,000 a year, and currently involves 12 staff and 1,000 children in curriculum work. Bands and orchestras meet on Saturdays in Galashiels.
Final decisions will be taken by the council's education committee on Tuesday. Mr Forsyth offered some financial leeway by agreeing to relax the Scottish Office cap on its spending, although this is not expected to yield a substantial amount of extra income through increased council tax.
Mr Christie said curriculum music was still in jeopardy. Knowledge of one instrument is essential for Standard grade and two for Higher and there are few private tutors in the area. Restrictions on what could be accomplished in the classroom meant brass and woodwind instruments were unlikely to be available, he said.
George Kynoch, the local government minister, announced the specific grant option during the Grand Committee debate but said money would have to come from other budgets through "top slicing".