The Morrison government's changes to higher education funding face rejection by the Senate, with key crossbench votes lining up to oppose the plan and a deal with the Centre Alliance now critical.

Crossbencher Jacqui Lambie has issued bruising criticism of the case made by Education Minister Dan Tehan for the shake-up — accusing the government of penalising poorer students as it increases the cost of humanities degrees in favour of degrees in areas including science, maths and healthcare.