Sunak is facing a critical test of his authority with politicians on the right and the left of the Conservative Party threatening to vote against the bill when it goes before parliament on Tuesday.
Last month, the UK Supreme Court declared the government's scheme to deport thousands of migrants to Rwanda unlawful, saying the east African nation could not be considered a safe third country.
In response, Sunak agreed a new treaty with Rwanda and has brought forward emergency legislation designed to override domestic and international human rights law which would prevent deportations.
However, one group of lawmakers said that the legislation did not go far enough in restricting appeals from asylum seekers and only provided a "partial and incomplete solution," underscoring the threat to the prime minister.
They said the bill did not do enough to stop migrants bringing individual claims stating Rwanda was an unsafe country, nor to stop the European Court of Human Rights from being able to interfere.
'Pull the bill'
It would only take about 30 Conservative members of parliament (MPs) to vote with opposition parties on Tuesday to defeat the bill.
Mark Francois, chair of one critical grouping within the party, told reporters the government would be "best advised to pull the bill and to come up with a revised version that works better to this one, which had so many holes in it."
For Sunak, struggling to revive a weak UK economy and heavily trailing the main opposition party in opinion polls, the Rwanda policy has become a defining issue for his government, despite lawyers saying at every stage that it would not work.
Defeat in Tuesday's vote would be a hammer blow for the scheme and severely weaken his premiership, with the Conservatives behind the opposition Labour party by about 20 points in opinion polls.
Even if the legislation is passed on its first vote in parliament, Sunak could still face attempts to toughen it up with amendments at a later stage.
More moderate Conservatives, who have expressed opposing concerns that the legislation risks breaching Britain’s obligations under the European Convention of Human Rights, will also meet later on Monday to discuss how to respond.
A spokesman for Sunak earlier said the government remains "confident" in its approach and it will continue to have discussions with lawmakers.
"We continue to listen carefully to MPs, we are confident this is the toughest version of legislation that will enable us to stop the boats," he said.
The government's own legal advice produced on Monday said its policy was "tough but fair and lawful" and that it sought to uphold international obligations while accepting it was a "a novel and contentious policy."
"There are risks inherent in such an innovative approach but there is a clear lawful basis on which a responsible government may proceed," the advice said. "A bill that sought to oust all individual claims would not provide such a basis."
But critics within his party painted a bleak picture of the chances of the legislation's success, although they did not immediately say if they would vote down the bill .
Danny Kruger, from the New Conservatives grouping in Sunak's party, said "the bill doesn’t yet work and we’re hopeful that the government will come forward with improvements."
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