Australian National University higher education expert Andrew Norton said the introduction of a funding floor was sensible and would give universities more confidence to expand enrolments without fear of losing government support.

Professor Norton said there was never a clear rationale for social work studies costing $14,500 a year so the concession was logical. But he warned the changes to both social work and psychology fees would introduce more complexity because funding levels were based on study discipline,not occupational outcomes.

"The tertiary access payment change is a mistake,"he said."Outer regional and remote students should be supported to go to the university that best meets their needs. It should be a regional student support measure,not a regional university support measure."

Labor education spokeswoman Tanya Plibersek said the government should dump the entire package and noted fees for social work and psychology courses would still increase by more than $1000 a year from current levels.

"You just can’t trust the Liberals with universities. When it comes to unis,all the Liberals know how to do is jack up fees and lock students out. Their latest announcement is no different,"she said.

A"Save Social Work"campaign launched by the Australian Council of Heads of Schools of Social Work urged the government to confirm in writing that no social work student would pay more for their degree.

"Any failure to do so would be a slap in the face for those social workers providing essential services to those in need,including victims of COVID-19 and the recent bushfires,"a spokesman said.

The Regional Universities Network said the government had addressed all its concerns. It called for the legislation to pass Parliament as soon as possible,saying the sector needed certainty and would need time to implement the changes for 2021.

"We are now very happy with these changes and RUN doesn't see the need for it to go to a Senate committee but parliamentary process will take place as the parties wish and we just hope it's not a protracted process,"RUN executive director Caroline Perkins said.

Vicki Thomson,chief executive of the Group of Eight universities,said the amendments were sensible but did not go far enough.

"Importantly,they provide some funding certainty which was previously missing. However,the underlying issues remain. We are being asked to teach more students with less support at a time when,collectively,the Group of Eight is facing a $2 billion revenue downgrade in 2020 and most likely worse to follow in 2021,"she said.

Australian Technology Network of Universities executive director Luke Sheehy said the funding floor addressed a key concern but the significant legislation still needed the scrutiny of a committee.

Mr Sheehy also criticised the changes to the tertiary access payment,saying the package should be about"supporting students and listening to their needs,not about supporting particular universities".

The bill is likely to be referred to a Senate committee andkey crossbenchers have raised a series of concerns about the funding overhaul.

In the party room meeting on Tuesday,Mr Tehan also made clear to Coalition MPs that existing students would not face fee hikes because the legislation would grandfather the changes.