Uni reform opponents want Pyne to go

With higher education reforms killed off in the Senate for a second time, the focus is now turning to the future of Education Minister Christopher Pyne.

Labor and independent senator Jacqui Lambie want the minister to go.

Opposition higher education spokesman Kim Carr says the minister's relationship with the Senate is now poisonous, after the upper house rejected his legislation 34-30 on Tuesday night.

Just three of the crossbenchers voted with the government when it needed support from six of them.

Mr Pyne insists he'll bring the reforms back to parliament for a third time, probably in June.

"This minister's bluff, his bluster, his bravado simply leaves people cold," Senator Carr told ABC radio on Wednesday.

"It is time for him to consider his future and if he doesn't then he should be sacked."

Senator Lambie said Mr Pyne - who's labelled himself a "fixer" on education policy - had failed despite using everything from blackmail to pushing university vice-chancellors into a corner.

But Prime Minister Tony Abbott is standing by his minister.

"He's doing a really, really good job. Of course he is," he told Fairfax Radio.

Government Senate leader Eric Abetz lamented there was undue concentration on how the crossbenchers voted when the focus should have been on Labor and the Greens.

Labor was arrogant to think it knew better than vice-chancellors what was good for the tertiary sector, he said.

The government still intends to pursue its reforms, but Mr Abbott hinted the next attempt to get them through parliament might come with more changes.

Universities Australia was pleased the government would persist but cautioned against making further arbitrary cuts to the sector in the May budget.

Greens leader Christine Milne said the crash-through-or-crash approach just showed the government wasn't learning from its failure to convince the Senate.

And Labor piled on, with MP Ed Husic saying the reforms clearly were just in suspended animation.

"It's definitely the Frankenstein bill, it's got bolts in the neck," he said.

"It will be scaring children in years to come."

Liberal Democrat David Leyonhjelm, who supported the government on Tuesday night, said the minister needed to explain the reforms better to crossbenchers who didn't understand what it would mean for their children and grandchildren.

But Senator Lambie said there had been enough talk.

"We have been listening. That's why the deregulation hasn't got through."