Boyle and Webber said the recruitment and retention of quality, homegrown, teaching staff and addressing workload and pay issues required money.
"For the Government to say there's no more money over and over, and it's up to us to shuffle the deckchairs, is frustrating to say the least," Boyle said.
"I don't like being forced to put a price tag on a child's education but unfortunately that's what it looks like the Government is asking us to do."
Industrial action was not something the teachers wanted to do and the PPTA hoped to avoid it, "but we cannot wait," Boyle said.
"I hope that we can continue to bargain in good faith and avoid it."
The Education Ministry has offered 3 per cent a year for three years, or 9.3 per cent by November 2020.
The PPTA had been holding meetings with members nationwide since November 7 to discuss the offer, concluding today.
The proposed 9.3 per cent rise would lift beginner secondary teachers' base salaries from $51,200 to $55,137 and base salaries for those at the top of the scale from $78,000 to $85,233.
Boyle said there was so much daylight between what the ministry was offering and what teachers wanted that it was "almost a failure of the moral responsibility to ensure that young people have got great teachers".
Education Minister Chris Hipkins issued a brief response.
"We welcome PPTA back to the negotiating table, which is scheduled to happen next week," he said.
Education Ministry Deputy Secretary Ellen MacGregor-Reid the ministry was "surprised" the PPTA was already threatening strike action next year as it still had four days of agreed bargaining to go before the end of the year with the ministry ready to schedule more.
"We are focused on doing everything we can to settle these negotiations and minimise disruption for students and parents - and we look forward to progressing talks with the PPTA next week," she said in a statement.
Last week the PPTA and its primary school counterpart the NZ Educational Institute (NZEI) agreed to join forces in their campaign for better pay and conditions for teachers if their wishes were not met.
Primary teachers are also in the midst of ongoing negotiations, having also rejected a similar offer.
Up to 30,000 NZEI members took part in nationwide strikes last week.
They are now in the process of considering the latest offer from by the Government, the outcome of which will not be known for a number of weeks.
Both unions, which represent up to 48,000 principals and teachers nationwide, said should the offer be rejected and no satisfactory offers made before term one next year, the unions would take joint action.
Key issues for the unions are recruitment and retention of teachers, workload and the pay offer itself.
