More than two-thirds of those questioned in a Harris poll supported industrial action, short of strikes, over class sizes and nearly a quarter said they would support strikes.
The poll suggests that the public are more enthusiastic about industrial action than teachers. Only half of teachers questioned in a survey of 5,000 schools by the moderate Association of Teachers and Lecturers (ATL) wanted to take part in industrial action.
The findings make alarming reading for the Government as Kenneth Clarke, the Chancellor of the Exchequer, tries to keep education spending down in this year's Budget.
The Harris poll of a representative sample of 1,015 adults commissioned by ATL shows that teachers have won widespread support for their campaign against spending cuts and rising class sizes.
More than 1 million primary school children were in classes of more than 30 before this year's spending cuts took effect and the number is expected to rise this term.
The poll shows that the public back teachers over the number of pupils in each class, with one in nine believing each should have fewer than 31 and one in three thinking they should be no more than 20. More than one-third say class sizes should be between 20 and 25 and 24 per cent that the limit should be between 26 and 30.
However, only 13 per cent were in favour of children in oversize classes being sent home.
Peter Smith, the union's general secretary, said: "The spiralling size of classes around the country looks set to be a key issue in the run up to the next general election. Politicians dismiss this at their peril.
"Most teachers do not favour strike action but remain convinced that they need to continue the campaign to lower class sizes. If the campaign fails, they know that some sort of industrial action, short of a strike, will carry the support of over two-thirds of the electorate."
More than two-thirds of those in the union's survey did not want to strike over class size but more than half said they expected classes to be bigger this term.
All three teacher unions sanctioned ballots on local industrial action over class size at their Easter conferences but none has so far taken place.
The unions are negotiating with headteachers and governors to try to solve the problem but Nigel de Gruchy, general secretary of the National Association of Schoolmasters/ Union of Women Teachers said: "There are no preparations for action over class size in any schools at the moment but it may not be far away."
Mr de Gruchy has suggested that children from oversize classes might be supervised in the playground or sent to the head's study if problems over large classes cannot be resolved.
Fieldwork for the poll was carried out from 8-10 September.Reuse content