Labor's education spokeswoman Tanya Plibersek has urged universities to oppose a funding overhaul after the eight biggest institutions signalled conditional support.
The proposal more than doubles the cost of some humanities courses in a bid to encourage people to enrol in courses the government argues lead to higher employability.
Science and maths would be among the degrees made cheaper, along with agriculture, environmental sciences and health.
Group of Eight chair Margaret Gardner told a parliamentary inquiry this week significant amendments could make the bill workable.
Ms Plibersek said she understood universities were under pressure from dwindling profits due to funding cuts and coronavirus.
But she couldn't imagine a high school principal agreeing with anything that would hurt students.
"University bosses need to be a bit more high school principal and a little bit less CEO in this instance," she told the ABC on Thursday.
The sector is under immense pressure, with the Australian National University and the University of NSW announcing major jobs losses on Wednesday.
While around 250 ANU staff have taken voluntary redundancies, a further 215 will go over the next nine months.
UNSW, which has also accepted voluntary redundancies, will axe a further 256 staff as it deals with similar cost pressures.
Ms Plibersek said the bill before parliament would rip more money out of universities as they grapple with a loss of revenue from international students.
"If coal or gas or iron ore were facing this huge hit to their revenue, the government would be there to help with JobKeeper," she said.
"University bosses should be demanding that the government step in and help."
Australian Associated Press
