The Abbott government's overhaul of universities has been defeated in the Senate.

The Senate voted down legislation to deregulate Australian universities, 33 to 31, with Labor and the Greens winning the support of Palmer United Party senators and independent Jacqui Lambie.

The government had been chasing support for the controversial bill, agreeing to multiple changes to convince key crossbench senators to jump on board.

Education Minister Christopher Pyne has foreshadowed a new reform package, which he said will be sent to the Senate early in the new year.

In a statement, Mr Pyne said the new legislation will include amendments proposed by crossbench senators, such as a push by Family First Senator Bob Day to keep HECS indexation at CPI.

He said it will also include a university transition fund and a scholarship scheme targeted towards disadvantaged and rural and regional students, “of keen interest to Senator Ricky Muir”.

“The Senate will gave the Christmas holiday period to consider this new reform bill,” he said.

In a later address to Universities Australia, Mr Pyne reiterated his comments.

"Those of you who think the Government will give up on this reform – you don’t have to worry, we certainly won’t be giving up on this reform," he said.

"Tomorrow I intend to introduce a new reform bill. The new reform bill will keep all of the elements of the current bill that has been defeated.

"So, round one is over, round two begins.

"This will happen – it will happen next year and I will continue to advocate for it."

'Pyne is embarrassing himself and needs to stop harassing me'

Mr Pyne had tried to negotiate with the Palmer United Party, but the party's leader in the Senate Glenn Lazarus said he was "not prepared to horse trade".

"Christopher Pyne is embarrassing himself and needs to stop harassing me and other crossbenchers," the Queensland senator said in a statement on Tuesday.

"I am being inundated with text messages from Christopher Pyne virtually begging me to support the Abbott government's higher education reforms.

"... I won’t be bought and I am not prepared to horse trade."

Opposition Leader Bill Shorten described the rejection of the bill as "another humiliating defeat" for Prime Minister Tony Abbott.

"We’ve won this round," he said.

"This is a sweet victory for everyone who has fought Tony Abbott’s plans for $100,000 degrees."