A teacher says schools are buying their own ventilators while waiting for 7,000 devices promised by the government.
Louise Atkinson, who is also a Carlisle city councillor, said the planned number of units may not be enough.
"Nobody wants to go back to [remote learning] but schools and colleges can't fight a pandemic in the classroom on their own," she said.
Carlisle Conservative MP John Stevenson said the government was doing all it could to fight the spread of Omicron.
"The government monitors, with advice from experts, exactly what's going on within schools and hospitals and the wider economy," he said.
"I accept it'll be a difficult few weeks but I think the government is doing all it can."
Competing for ventilators
Six education unions called on the Department for Education to take action on ventilation in schools in August and warned of a steep rise in Covid and long Covid when pupils returned to classes in September.
Ms Atkinson, who is also vice president of the National Education Union (NEU), said air filtration devices were essential to halting the spread of the virus.
"We know across Carlisle and Cumbria headteachers are buying these from school budgets," she said.
The NEU councillors network sent an open letter to the education secretary, Nadhim Zahawi, on Friday calling on him to roll out filtration devices to all schools, the Local Democracy Reporting Service said.
Education leaders should not have to "compete with other schools to obtain the few available devices", it said.