Back in May, the Education Minister unveiled the plan to gradually increase student fees from next year and to make students start repaying their HELP loans once they are earning $42,000 a year, down from the current threshold of around $55,000.
Under the changes, universities will also be hit with a 2.5 per cent efficiency dividend for the next two years and some funding will be contingent on performance in areas such as student retention.
With Labor and the Greens opposed, the Government needs 10 of the 12 Senate crossbenchers to get its plan through.
Here is what we know so far about the way the crossbench is thinking.
Liberal Democrat David Leyonhjelm
Is the only confirmed yes vote at this stage.
But it comes with a condition attached. He will only support the bill as long as it is not watered down during negotiations with the Nick Xenophon team.
So that puts a big question mark over his support.
The Nick Xenophon Team
Nick Xenophon and his team hold three votes in the Senate, so the Government cannot succeed without them.
The party has been heavily focused on media laws so far this week and will turn attention to higher education once that is dealt with.
That means a vote could be delayed and pushed out until the next sitting in a month's time.
One Nation has four votes in the Senate and at this point has not declared its position.
But earlier this year, Pauline Hanson called on the Government to make students start repaying their HELP loans once they start earning $22,000 a year.
The Government will not agree to that.
Australian Conservatives Cory Bernardi
Senator Bernardi also wants changes to the package.
He says he wants to save taxpayers' money and will try to make some improvements.
He is concerned about penalties for private institutions and wants to make universities more accountable when it comes to the job prospects of their graduates.
Jacqui Lambie Network
Senator Lambie is concerned about several elements of the package but willing to talk to the Government.
In particular she is worried about students having to pay higher fees.
She is also concerned about a decision to start charging students for enabling courses.
These courses help students prepare for university. Under the changes, institutions will be able to charge more than $3,000 and she is worried that will deter students from low income backgrounds.
Derryn Hinch's Justice Party
Senator Hinch said the Government has not spoken to him yet, but he will not support the change to make students start repaying their HELP loans once they earn $42,000.
He said he would agree to $50,000 but no lower.
He also doesn't want to see any cuts to funding for institutions in regional Victoria.
Independent Lucy Gichuhi
Is still receiving briefings from the Government and has not decided.