Johnson returned from an EU summit in Brussels overnight for what is expected to be a busy day attempting to persuade lawmakers to vote for the divorce deal at a rare Saturday sitting of Parliament.
It is expected to be a knife-edge vote.
Johnson's Conservative Party holds only 288 seats in the 650-seat House of Commons so he will have to rely on support from other parties and independent lawmakers to get over the line.
Foreign Secretary Dominic Raab started drumming up support early.
"We've got a real opportunity now to get Brexit delivered faithful to the referendum, move on as a government, and I think as a country, and lift the clouds of Brexit," he told the BBC.
Raab said the government has not given up hope of winning the support of its Northern Ireland ally the Democratic Unionist Party, which has rejected the new deal.
But the chances of that appeared slim. The DUP's Brexit spokesman, Sammy Wilson, said Johnson's Brexit package — which carves out special status for Northern Ireland to keep an open border with EU member Ireland — is bad for his region and its bonds with the rest of the U.K.
"I can give you absolute assurance we will not be voting for this deal when it comes before the Commons tomorrow," he told the BBC.
The deal's fate could largely rest on a group of former Conservative Party members expelled from the party earlier this year for voting against the government, and members from the main opposition Labour Party, which has 244 lawmakers. Labour leaders have told party lawmakers to oppose the deal. But around 20 of them, mainly representing pro-Brexit parts of the country, have previously indicated a desire to back a deal in order to honor the June 2016 Brexit referendum result.
Not even expert analysts can gauge the exact numbers.
"There seems to be an indication that it will be very, very close, it will come down to one, two or five people," said Joelle Grogan, a senior lecturer in U.K. and EU law at Middlesex University. "But speaking only with 24 hours away, I have no idea what that will look like."
If Johnson's charm offensive manages to corral enough votes to pass the deal, Britain would be on course to leave the EU in an orderly fashion on Oct. 31 — though Parliament would still need to pass legislation to implement the decision.
If lawmakers reject the deal — as they did three times with an earlier deal presented by Johnson's predecessor Theresa May — a law passed earlier this year compels the prime minister to ask the EU for another delay to Britain's exit date.
Johnson has said he won't do that, but also that he will obey the law, an apparent contradiction.
Asked Thursday what he would do if Britain seeks an extension, European Council President Donald Tusk said he would consult the other 27 EU nations in order to reach a decision — leaving open the prospect of another delay.