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.
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, which has called for stronger measures to cut immigration, 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 on Tuesday.
Members of the group are due to meet Mr Sunak on Tuesday morning.
Earlier, the European Research Group (ERG) – 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 – and “very significant amendments” would be needed.
The group has not yet decided how to vote on Tuesday.
Following a meeting of the ERG and several other backbench factions, the group’s chairman Mark Francois said: “The feeling very much in the meeting is that the government would be best advised to pull the bill and come up with a revised version that works better than this one – which has 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.
However, 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, said: “We have taken the decision that the most important thing at this stage is to support the bill – despite our real concerns.
“We strongly urge 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.
To vote against the bill at this stage would be a vote against the principles of the legislation rather than just its details. Many Tory MPs would be extremely reluctant to do this and may prefer to abstain.
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 – despite the One Nation group warning against some of these.
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.”
Another MP on the right said: “I’ll vote against if enough colleagues are going to do that to defeat the government. But if just a few want to vote against then I’ll abstain.”
If the rebels went through with voting against the government in large enough numbers this would be near-apocalyptic for 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.
But the possibility of these consequences may well be enough to give many of the potential rebels pause for thought.
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”.
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.