Draft laws, which include extending the waiting time for permanent residents to apply for citizenships, tougher English language tests and extra powers for the minister, are listed among legislation to be debated this week.
The Senate has given the government until Wednesday to allow debate on its legislation or have it struck out by default.
"It's looking awfully like Peter Dutton has thrown up the white flag on his white Australia policy and this is a great day for multicultural Australia," Greens senator Nick McKim told reporters in Canberra.
The proposed changes appear likely to fail, with Labor and the Greens opposed and the Nick Xenophon Team signalling it will not support the bill in its current form.
If debate does not get underway by Wednesday evening, the legislation will be removed from the Senate notice paper, requiring the government to win a motion to restore it at a later stage.
Labor leader Bill Shorten said the proposed citizenship changes were patently unfair and ridiculous, suggesting the government go back to the drawing board.
Mr Shorten said the proposed requirement for university-level English competency - which the government has since agreed to water down - appalled working and middle-class migrants who had been in Australia for decades.
"I think the best thing they could do is just quietly drop the proposals," he told reporters in Canberra.
"Here's an idea for Dutton - maybe he should talk to us before he announces this stuff."
