Rishi Sunak is confident that his flagship Safety of Rwanda Bill will finally be passed this week.
The House of Lords will support some more amendments to the bill later today which will be overturned by MPs tomorrow.
Rebel peers are then expected to back down, paving the way for the legislation to finally become law.
The prime minister is optimistic that deportation flights to Rwanda will finally take off within weeks, providing a deterrent for any asylum seekers still tempted to cross the Channel in small boats.
Sunak hopes that will finally provide the spark to ignite a Tory comeback in time for the general election.
But polling by the More in Common think-tank has revealed that the chances of the Rwanda plan saving the Conservatives in time for polling day are vanishingly small.
Only 10% of voters believe that getting flights off the ground, even if it doesn’t stop a single boat, will be a success.
And nearly half - 47% - say they will only think the controversial policy is successful if it either significantly reduces small boat crossings, or stops them entirely.
Given that we are on course for a record number of crossings this year - with more than 700 making the journey last weekend alone - that seems like a forlorn hope.
Luke Tryl, UK director of More in Common, said: “It is quite clear that just sending flights is not enough for people.
“A clear plurality - including 60 per cent of 2019 Conservative voters - only think it will be a success if it significantly reduces Channel crossings.”
Tryl said there may be a “short term boost” for the Tories if they succeed in sending the first asylum seekers to Rwanda later this year.
But ahe added: “What is really going to matter - and I think what will be pivotal to the Conservatives’ fortunes, particularly with defectors to Reform UK - is that then over the summer we see that reduction [in crossings].”