Rishi Sunak is racing to shore up support for his Rwanda bill among right-wing MPs, ahead of a crucial vote later.
The PM has met potential rebels over breakfast in No 10, as he tries to convince them to back the legislation.
The bill seeks to revive the government's plan to send some asylum seekers to the east African country.
But some on the right of the party say a tougher law is needed to ensure the scheme works.
Meanwhile, Tory MPs from the more liberal end of the party say they will support it in its current form, but have warned against any changes further down the line, arguing they could breach international law.
It means Mr Sunak is facing the biggest challenge to his authority from his MPs, who could inflict humiliation on the PM over one of his key policies.
The government's legislation has been drawn up to revive the Rwanda scheme, after the Supreme Court ruled it unlawful last month over fears it could lead to human rights breaches.
The legislation seeks to declare in UK law that Rwanda is a safe country to send asylum seekers to, and stop flights being grounded for legal reasons.
However, some right-wing Tory MPs are concerned it does not go far enough to prevent further legal challenges derailing deportations.
At around 19.00 GMT, MPs will be asked to decide whether the bill should be allowed to progress to its next stage in Parliament.
With Labour and other opposition parties opposing the bill, a revolt by 29 Conservatives voting against the bill would be enough to defeat it at this early stage - something that has not happened since 1986.
Labour leader Sir Keir Starmer says he will scrap the Rwanda plan if his party wins the next election, arguing the £290m due to be given to the east African country as part of the scheme would be better spent on UK police.
Tory factions meet
Ahead of the vote, several senior Tories, including former defence secretary Ben Wallace and attorney general Sir Geoffrey Cox, have called on MPs to unite, warning disunity would spell disaster for the party ahead of the next election.
"If we go on like this of course we're going to switch off millions of people upon whose votes we depend," Sir Geoffrey told OceanNewsUK Newsnight.
The New Conservatives group, whom Mr Sunak met on Tuesday morning, has said the bill requires "major surgery or replacement".
After a meeting on Monday evening, several MPs in the group said they were deciding between abstaining or voting against the bill.
The European Research Group - another group on the party's right - has argued "very significant amendments" are needed to prevent legal challenges to Rwanda deportations.
Agreeing to the demands of MPs on the right of the party would risk losing the support of more centrist Tories, however.
The One Nation group, which includes more than 100 Tory MPs, said it was recommending its members vote for the bill at this stage, but warned it would oppose any future amendments "that would mean the UK government breaching the rule of law and its international obligations".
Tory critics could decide to allow the bill 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 at 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 OceanNewsUK. "It's now or never."
Going ahead with the vote and being defeated would potentially presage a leadership election for Mr Sunak, 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.
Those who want the Rwanda bill to go further argue it could still leave the scheme open to legal challenge by individuals, who could argue deportation to Rwanda would put them at risk of serious harm.
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 advice argues that the grounds for individual challenges to deportation will be "exceptionally narrow" under the bill, and a blanket ban on appeals would breach 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.
