CANBERRA, Sept 12 - But Education Minister Simon Birmingham wouldn't commit to pushing for a vote before the Senate rises on Thursday.
"Go to a bookie if you want some odds, not me," he told ABC radio on Tuesday, ahead of debate resuming in the lower house.
It's expected legislation will get to the Senate on Wednesday.
"In the interests of providing certainty to students, to universities, to others, we would like to see these matters dealt with this week," Birmingham said.
"Whether the Xenophon team are ready to deal with it this week, whether the rest of the crossbenchers are ready to deal with it this week, we'll see. I'm a very hopeful kind of guy."
The government wants to cut university teaching funding in 2018 and 2019, raise student fees, lower the repayment threshold for student loans, and tie a portion of funding to performance measures such as student retention.
The higher education sector is opposed to the changes, saying they will lead to students paying more but getting less.
Universities Australia released polling on Tuesday showing just one in six Australians supported the cuts while nearly four in six opposed them.
"This confirms that the government's plan to impose a $2.8 billion cut on universities and students is way out of kilter with community sentiment," Universities Australia chief executive Belinda Robinson said.
Birmingham dismissed the polling.
"Given how loaded the question that was asked was, I'm surprised support's even that high,' he said.
He argues universities won't have funding cut, just a lower rate of growth than without the changes, and will still see a 23 per cent increase over the next four years.
Labor and the Greens oppose the changes, meaning the government has to rely on the Senate crossbench to pass the legislation.
The Nick Xenophon Team, which has three of the 10 votes the government needs, is yet to decide its position but has flagged serious concerns with the package.
Conservative crossbenchers David Leyonhjelm and Cory Bernardi have warned the government it will lose their votes if it waters down the cuts too much to win NXT support.