Disgruntled figures within the Australian Greens have accused the teachers' union of putting politics before children by threatening to campaign against the party if it supports the government's plans to boost school funding.

Pressure from the union has split the Greens, leaving them paralysed and the government increasingly reliant on the Senate crossbench to secure the passage of its Gonski 2.0 reforms which would inject an extra $18.6 billion into schools on a needs basis over the next decade.