Despite earlier opposing a Senate committee look at the draft legislation overhauling university fees, the government has agreed to about a three-week probe.

The Senate's education and employment legislation committee has until September 25 to run an inquiry on the bill.

It paves the way for the bill to be debated in parliament during the October 6 budget sitting week.

Labor and the Greens had pushed for a longer inquiry, until November 30.

The proposed laws would more than double the cost of some humanities courses in a bid to encourage people to enrol in courses the government argues lead to higher employability.

Science and maths would be among the degrees made cheaper, along with psychology, agriculture, environmental sciences and health.

Labor's education spokeswoman Tanya Plibersek has accused the government of being dragged kicking and screaming to the inquiry.

"Whenever there are tough questions to answer, the Liberals run from scrutiny," she told AAP on Thursday.

"If Scott Morrison thinks his plan to cut unis and jack up fees is so great, why did he try to stop an inquiry for so long, and why is he trying to rush it now? What is the prime minister trying to hide?"

A vote in the Senate earlier this week showed a lack of majority support for the bill, questioning the future of the fee reforms.

Australian Associated Press