Addressing the union's annual conference in Perth yesterday (Thursday), Moira McCrossan called on ministers, employers and unions to shift their entrenched positions to reach a deal.
The EIS backed much of the Government's agenda, including its emphasis on social inclusion, Ms McCrossan said.
"I am not suggesting we should abandon our conditions of service or that teachers alone should bear the responsibility of delivering social inclusion.
"But if we are urging genuine partnership on the Government and a commitment to listen, we must be prepared to examine our own sacred cows and consider whether or not they still serve us well."
She warned: "If the millennium negotiations founder, the Government may well be able to drive through its modernisation agenda in the teeth of teacher opposition. Eventually teachers may fulfil whatever new responsibilities are enforced, grudgingly without commitment or ownership.
"The losers will be all of us but especially the children. We all need to be prepared to shift our positions.
"Some of the ideas before us are ill thought out and educationally barren. We need to identify these and relentlessly point out the flaws. But there are large areas where we are in complete accord with the Government's intentions, differing only in terms of detail."
Ms McCrossan argued that the EIS had won the battle over post-16 curricular reform, describing the solution agreed in the Higher Still Liaison Group as "a model of reasonableness on all sides".