Head teachers could bring in a four-and-a-half day week in schools around England as they grapple with £3bn in budget pressures.
Heads at the National Association of Head Teachers conference said ministers had not been listening to their plight.
They backed a motion giving their leaders licence to explore all available options - including a shorter school week - to protect education.
The government insists school funding has never been higher.
It says funding will rise to £41bn in the next year.
Head teacher Graham Frost said at the conference in Telford that the line from the government was like "a recorded message" that came back every time the issue was raised.
"We are not advocating a four-and-a-half day week, we are just so despairing," said Mr Frost.
He said dropping teacher hours could be necessary if a school did not have the staff to run classes safely.
Alternatively, a head may make this decision to prevent schools from axing support staff for children with particular needs.
The motion also gave the NAHT executive the right to encourage its members to take other steps, such as running deficit budgets in schools or refusing to file budgets to local authorities.
The NAHT will discuss further steps in its campaign to oppose school funding cuts at an executive conference in June.
The National Audit Office has found schools are facing budget cuts of £3bn by 2020 because funding was not keeping pace with increased pupil numbers and the rising costs of national insurance and pension contributions.
