The Senate has voted down the Federal Government's legislation to uncap university fees, the second time the Coalition's higher education changes have been rejected.

Labor and the Greens were joined by several crossbench senators to defeat the bill 34 votes to 30.

Independent senators Nick Xenophon, Jacqui Lambie and Glenn Lazarus, Ricky Muir from the Motoring Enthusiasts Party, and Palmer United Party senator Dio Wang opposed the Higher Education and Research Reform Bill.

Family First senator Bob Day supported the bill, along with Liberal Democrat David Leyonhjelm.

Independent senator John Madigan also voted in favour of the bill but made it clear he wanted it to progress so that it could be amended.

"I have serious concerns with the bill in its current form, but I also fear the consequences of doing nothing," he told the Senate.

Senator Xenophon said everyone agreed the system of university funding needed to change.

"I don't, however, believe that deregulation is necessarily to best option in solving this problem," he said.

"I cannot accept what the Federal Government is doing. I cannot support it."

Senator Xenophon said he welcomed the Government's recent changes to the legislation as a sign of willingness to listen and compromise.

"[Education] Minister Pyne is incredibly flexible," he said.

"More flexible than a yoga instructor, I think sometimes."

The Assistant Minister for Education, Simon Birmingham, told senators the Coalition's proposal was the best option on the table.

"The higher education system must be adequately funded to ensure quality and sustainability, and the deregulation of fees provides the most realistic way to do this," he said.

Change in tactics fails to secure needed Senate support

On Monday, Education Minister Christopher Pyne announced he would split the original legislation, sidelining a $1.9 billion funding cut to course fees which he said would be considered "at a later time".

Mr Pyne also backed down on his threat to withdraw $150 million for research unless the Senate passed the higher education package, declaring it had been a "distraction".

But the dramatic shift in tactics has failed to change the vote in the Senate and it is unclear what Mr Pyne may do next to try to bring in the changes to the university system.

The concessions proposed by My Pyne would have put further strain on the federal budget of around $1.4 billion, particularly through an extension of student loans to TAFE and college students.

That was instead of a $3.9 billion saving when the package was announced at budget time.

After Tuesday's vote, Mr Pyne said the Government remained committed to education reform.

"Few dispute that without reform, Australia's higher education system will steadily decline," he said in a statement.

"We will therefore bring back the higher education reform package for the Parliament to consider. We will not give up. This reform is too important.

"We will continue to work with senators and others who wish to be part of a constructive discussion."

Opposition Leader Bill Shorten said Labor would continue to "fight the Americanisation of our university system".

"Tonight's vote is yet another humiliating failure for Christopher Pyne, who has lost all credibility with the Australian people as a result of his so-called negotiations, which were based entirely on bullying and blackmail," he said in a statement.

"It is time for Christopher Pyne to accept that he introduced a bad policy and got a bad result for the Government."

It's just a matter of priorities: Lambie

Some of the Coalition's opponents called for more public spending on tertiary education.

Greens leader Christine Milne told the Senate that changes to taxation of superannuation and fuel could help fund education.

Senator Milne drew on her personal experiences in explaining why the Greens were opposed to allowing universities to set their own fees.

"I know what's it's like to be fronting that fact that you may not be able to go to university because you can't afford it," she said.

Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume. Watch Duration: 11 minutes 6 seconds 11 m Senators David Leyonhjelm and Jacqui Lambie join 7.30

Senator Milne said she would not have got a tertiary education if it were not for the assistance of scholarships.

"That is precisely the case for so many people and that is why deregulation is so wrong."

Senator Lambie called for funding for higher education to be increased to 1 per cent of GDP, telling the Senate "the money is there - it's just a matter of priorities".

She suggested the Government cut the foreign aid budget instead or redirect funding going to states for privatising their assets.

Senator Lambie criticised both Labor and the Coalition for cutting funding to universities in recent years, but was particularly scathing of the current Government.

She said "they want to make us more like America" and entrench "a blue-tie aristocracy".