Prime Minister Rishi Sunak is facing a battle to persuade Tory MPs to back his flagship Rwanda bill, ahead of a key vote on Tuesday.
The legislation seeks to revive the government’s plan to send some asylum seekers to the east African country.
MPs on the right of the party have said the bill does not go far enough and will not work in its current form.
But more centrist MPs warned against any changes which would breach international law.
Former Defence Secretary Ben Wallace urged his fellow Tory MPs not to “wreck” the government by voting down the bill.
Writing in the Telegraph, he warned against “making the perfect (but unrealistic) the enemy of the good”.
Former attorney general Sir Geoffrey Cox told BBC Newsnight that “if we go on like this of course we’re going to switch off millions of people upon whose votes we depend”.
He told the programme: “This bill is the beginnings of the solution to the problem… We need to unite – improve it – but get it through.”
The Safety of Rwanda Bill faces its first Parliamentary test – known as its second reading – on Tuesday, when MPs get a chance to debate and vote on the main principles of the bill.
The aim of the policy is to deter migrants from crossing the Channel and it is central to the government’s plan to “stop the boats” – which Mr Sunak has made one of his key priorities.
A rebellion by Tory MPs could sink the Rwanda scheme and severely damage the prime minister’s authority.
Among those on the right of the party, the New Conservatives group said the bill required “major surgery or replacement”.
More than 40 members met on Monday evening to discuss how they would vote. Several MPs leaving the meeting said they were deciding between abstaining or voting against the bill. Two MPs said the group had the numbers to vote the legislation down and that only one or two in meeting had spoken in support of voting for the bill.
Members of the group are due to meet Mr Sunak on Tuesday morning.
Earlier, the European Research Group – an influential group of Tory MPs also on the right of the party – said the bill provided an “incomplete solution” to the problem of legal challenges that could be mounted against individuals being sent to Rwanda. It said “very significant amendments” would be needed.
The group has not yet decided how to vote on Tuesday.
Its chairman Mark Francois called on the government to pull the bill and come up with a revised version without “so many holes in it”.
However, agreeing to the demands of MPs on the right of the party would risk losing the support of more centrist Tories.
Following a meeting on Monday evening, the centrist One Nation group of Conservative MPs, which includes more than 100 MPs, said it was recommending its members vote for the bill at this stage.
But the group said it would oppose any future amendments to the bill “that would mean the UK government breaching the rule of law and its international obligations”.
The group’s chairman, former Deputy Prime Minister Damian Green, urged the government to “stand firm against any attempt to amend the bill in a way that would make it unacceptable to those who believe that support for the rule of law is a basic Conservative principle”.
It is very rare for a bill to be defeated at its first Commons hurdle and this has not happened since 1986.
However, Labour and opposition parties have already said they will try and vote it down, meaning the government needs to ensure enough Tory MPs vote for it to allow it to pass.
Tory critics of the bill could decide to allow it to pass at this stage, possibly by abstaining, in the hope of securing concessions from the government as it goes through the Commons.
But some MPs who previously appeared inclined to back the government in Tuesday’s vote, in the hope of amending the bill at a later stage, now seem much more pessimistic about that possibility.
“There’s no way we’d have the votes to amend it next year,” one Tory MP told the BBC. “It’s now or never.”
If there are enough rebels to inflict a defeat this would be near-apocalyptic for Mr Sunak in political terms.
That prospect may be enough for him to withdraw the bill completely.
Going ahead with the vote and being defeated would potentially presage a leadership election, perhaps even a general election.
Those around the PM acknowledge the numbers are tight but say they are confident they can win and insist they are not going to pull the vote.
The government introduced the emergency legislation last week, after the Rwanda policy was ruled unlawful by the Supreme Court.
The bill seeks to stop flights being blocked on legal grounds, by declaring in UK law that Rwanda is a safe country.
Those who want it to go further argue it is still open to legal challenge by individuals, if they can provide compelling evidence their personal circumstances mean they would be at risk of serious harm if they were removed to Rwanda.
In an attempt to win over critics, the government took the unusual step of publishing a summary of its own legal advice on the scheme.
The document says the bill allows for “an exceptionally narrow route to individual challenge” – but that to block all court challenges “would be a breach of international law”.
It gives examples such as people in the late stages of pregnancy who are unfit to fly or with very rare medical conditions that could not be cared for in Rwanda.
However, critics argue that even if only some of these claims succeed, they would still clog up the courts and delay removals.
Downing Street said the government would continue to listen to the views of MPs but it believed the bill was “strong enough to achieve its aims”.