Labour is confident it can convince the majority of potential rebels to vote with their whip against the prime minister’s proposed Brexit deal, with a number of the party’s prominent Eurosceptics suggesting they would vote it down.

Tory sources had briefed that they believed up to 20 would back the government, but a number appeared to be already wavering on Wednesday, putting the deal at significant risk.

If the Democratic Unionist party vote against it then Theresa May would be reliant on Labour votes to get the deal through parliament.

On Wednesday night, the Labour party leader, Jeremy Corbyn, and chief whip, Nick Brown, met May for a 20-minute meeting after she briefed her cabinet, in order to discuss the run up to the vote. Corbyn tweeted after the meeting: “This is a bad deal which isn’t in the interests of the whole country.”

A Labour source said Corbyn had stressed importance of giving parliament and committees sufficient time and information for serious scrutiny of the deal and that Labour would put down its own amendment when the deal was put to parliament.

Key to Labour calculations have been the 15 Labour MPs who defied the whip in June to vote against an amendment to the EU withdrawal bill which would keep the UK in a Norway-style EEA agreement. MPs had been instructed to abstain on the amendment, though Labour eventually split three ways, with dozens more voting to back it.

Those 15 included prominent Brexiters, such as Kate Hoey and Dennis Skinner, but also MPs who have been vocal about the need to honour the result of the referendum in their leave constituencies, such as the Don Valley MP, Caroline Flint and the Stoke-on-Trent Central MP, Gareth Snell.

However, Skinner was understood to have told allies he would not back the prime minister’s deal. Another leftwing Brexiter, Graham Stringer, said he was “almost certain” he too would vote against.

Hoey has confirmed she would not back the prime minister, writing in a blogpost for LabourList that the deal was “pandering” to threats from the Irish government.

“At the end of the day, it will come down to what team you play for,” one Labour source said. “Our MPs are tribal and there’s not much the whips will need to say to make some people come to that decision on their own.”

Snell told the Guardian he would need significant reassurances about how the party would prevent a no-deal Brexit should MPs vote against. “The Labour party is committed to leaving the EU and that means the only option to no deal is leaving with a deal,” he said.

“If we vote down this deal, then we need to be clear: what we will do in the 12 weeks that follow to facilitate a new deal? We should be saying, in concrete terms, what we are going to do to prevent no deal. People like me need to have that reassurance.”

Frank Field, a Brexiter who resigned the Labour whip, also said he had yet to decide how to cast his vote. “I want to give a considered response and not commend or condemn it without having seen its contents,” he said. Field has previously said he was deeply concerned about the prospect of no deal.

MPs were likely to come under intense pressure from grassroots Labour members, the majority of whom are both keen backers of the Labour leader, Jeremy Corbyn, and against leaving the EU.

Momentum was to launch a campaign to persuade wavering Labour MPs, specifically targeted in leave-leaning seats where MPs were most likely to be torn. The Guardian understands that the pro-Corbyn blog Skwawkbox has also been emailing MPs to ask whether they would vote down the deal.

Momentum’s leadership has previously been reluctant to take specific positions on Brexit, but recently surveyed its membership and found more than 92% said they backed voting down any deal in parliament.

Anti-Brexit groups were also likely to ramp up the pressure. Best for Britain, fronted by the Labour peer Andrew Adonis, was set to target the constituencies of the party’s wavering MPs, producing Brexit impact assessments for them and giving them new election data to allow MPs to see the remain versus leave splits in their seats. Those seats would also be targeted with local paper adverts and posters.

“There are people who feel they need to signal to their constituents that they are not against Brexit,” another Labour source said. “But when this version of Brexit is going down so badly with hard Brexiters, it makes it difficult to square.”

Corbyn’s spokesman has made it clear that Labour’s first priority if the government’s deal fails to pass the Commons will be to press for its “different, alternative Labour plan for Brexit”.

Speaking to journalists after prime minister’s questions, he said if May lost the meaningful vote, Labour would consider it to be a vote of no confidence in the government, although formally, under the Fixed Terms Parliament Act, this would not be the case.

“Clearly, if the government is defeated on this absolutely central part of its programme, then it would have shown it was unable to govern, and unable to deliver the most essential priorities for the country.”

Corbyn irked many Labour members with an interview last week where he said “we can’t stop Brexit”. Pressed repeatedly on the question, his spokesman said the party was committed to carrying out the result of the referendum but a number of options remained on the table in the event May’s deal failed to pass.

“Obviously, from a technical point of view, Brexit can be stopped, that’s clearly the case,” he said. “But Jeremy said, ‘we can’t stop Brexit’. That’s not either our policy, nor our priority, nor do we have the mechanism to do it.”