Failure to pass the measure would be a blow for the government as it eyes a series of legislative wins before the Christmas break, but would not endanger the deal with the US to resettle refugees currently on Manus Island and Nauru.
It comes as the Department of Immigration confirmed at least 857 people had expressed interest in US resettlement, including some of the 377 people who have been temporarily transferred to Australia from Nauru or Manus Island for medical reasons.
That figure included 245 people who were adults when they were first sent to a regional processing centre, meaning they would be subject to the lifetime visa ban. The remainder were minors from about 90 family units and would not be barred for life from Australia.
The proposed ban would make any adult sent to Manus or Nauru after 19 July 2013 ineligible to make a valid visa application in Australia, including for business or as a tourist. Labor and the Greens have pledged to vote down the bill.
That makes the government reliant on an unpersuaded crossbench, and it is understood to have secured only five of the eight votes needed to reach 38: the four One Nation senators and Tasmania’s Jacqui Lambie.
NSW Liberal Democrat senator David Leyonhjelm said he would not vote for the current bill and is drafting two amendments: one to exempt temporary visas such as tourist visas from the ban, and another to exempt refugees from Australia’s direct neighbours, such as Indonesia and Timor Leste.
“If they leave that country and arrive in Australia with nothing in between … then we think the lifetime ban is unreasonable in those instances,” Senator Leyonhjelm said on Monday. He said the government was aware of his amendments but had not responded.
Of the Nick Xenophon Team, party leader Nick Xenophon is understood to be the most sympathetic to the ban, but is still holding out for concessions from the government. Senators Stirling Griff and Skye Kakoschke-Moore are expected to vote against the bill.
Victorian senator Derryn Hinch indicated he would carefully consider a Senate committee report on the matter, due to be filed on Tuesday, and declined to comment further. But last week, after attending a public hearing, he tweeted: “Banning people who [are] seeking asylum from ever visiting Aus is cruel and unnecessary.”
Senator Hinch’s staffer, Sarah Mennie, tweeted on Monday that the office had been “bombarded with [an] orchestrated campaign” from refugee advocates, to the point of diverting staff away from considering the legislation. “We hear you … pls stop,” she wrote.
A spokeswoman for Immigration Minister Peter Dutton said he would not provide a running commentary on any crossbench negotiations through the media. Mr Dutton and the Department of Immigration would not provide an update on the number of people who had expressed interest in US resettlement – the figure of 857 was current as of November 15.
Greens senator Nick McKim said the ban was unnecessary and achieved nothing except to create two classes of citizens, and should be blocked. “I’m not convinced the government has got the numbers,” he said.
The bill passed the House of Representatives on November 10 and Mr Dutton has said it is “likely” to be listed for debate in the Senate next week, the final parliamentary sitting week of 2016. He has called on Labor to reconsider its opposition to the ban.