In the social media swirl surrounding Saturday’s Brexit vote, one parliamentary correspondent noted he had seen Labour’s chief whip walk past carrying a large roll of black duct tape. On a day when every Labour vote was critical, it sparked bemused speculation as to what the tape was for: holding the party’s more wavering MPs hostage? Or just forcing Jacob Rees-Mogg to sit up properly?

Rebel Labour MPs want to support a Brexit deal either because they sit in a heavily leave-voting seat, are Brexiters themselves, or think it should happen because Britain (narrowly) voted for Brexit – or any combination of those three. We aren’t talking huge numbers – the government calculated it potentially had the support of some 15 Labour rebel MPs for Saturday’s non-vote. But things are increasingly tight and increasingly critical: Boris Johnson’s government is pushing an extreme Brexit and has decimated its narrow minority by alienating allies and its own MPs. Every time there’s a Brexit vote, there is a huge Labour operation to keep MPs on side. So far they have been successful, with Theresa May losing three meaningful votes on a Brexit deal, and Johnson’s version now being paused to allow proper scrutiny.

Trade unions in particular are sensitive to the feelings of those Labour MPs in leave constituencies who are conflicted

Stakes are high and many campaigners are, not unreasonably, frustrated that any Labour MP could support a Brexit deal that would be so damaging to workers and industry. Then there’s the added worry of how an extreme Brexit deal getting over the line with Labour votes would play in a general election. In light of this, attempts to persuade these wavering MPs may appear combative, but this does not necessarily reflect the tone found behind closed doors.

Some have called for the party whip to be removed from MPs voting with the government. The Momentum founder, Jon Lansman, who sits on the Labour party’s ruling body, the national executive committee, said that if MPs did support the Brexit deal, the NEC “will have no choice but to replace them with a new, socialist Labour candidate at the next election”. This has not happened over policy issues for decades, but some say extraordinary circumstances such as Brexit require extraordinary measures. The leader’s office disagrees, however – Jeremy Corbyn and his team tend to see this as an illiberal measure at odds with a progressive party and with a current leadership that is intent on democratising the party. One source close to the leadership noted that an operation constantly decried as Stalinist was now being criticised for not being purge-y enough.

With whips pressuring MPs, Corbyn and the shadow chancellor, John McDonnell, also put in phone calls to those who were unsure of how they would vote. During the parliamentary debate, the shadow Brexit secretary Kier Starmer’s forensic demolition of the government’s Brexit proposal was interspersed with references to Labour values. Other message carriers such as Labour left MPs Laura Pidcock and Dennis Skinner perhaps could persuade parts of the party that Starmer might not reach. Given the horrific impact of this deal on jobs and workers’ rights, the fact that all trade unions were hammering precisely this point, in public statements and videos as well as private conversations, was also key.

Labour MPs often insist, even in the midst of the most fractious infighting, that the party is like one big family. It might prompt sceptical eyebrow-raising, but this vision of a friendly, unshakeably tribal party seems to kick in during crunch times. Labour and union organisers alike say they would categorise only one or two Labour MPs as having made a “psychological departure” from the party, as one campaigner describes it. Meanwhile some MPs have already announced plans to stand down at the next election, so may be less persuadable.

Trade unions in particular – they all have members who voted leave – are sensitive to the feelings of those Labour MPs in leave constituencies who are conflicted. “The aim throughout is to achieve the best possible outcome for working people and that’s what most Labour MPs want, too,” a union source told me. Some campaigners say that, in the midst of a poisonous and threat-filled political climate, potentially rebellious MPs are already feeling isolated and embattled, so assuring them of support – particularly for tough elections in constituencies with high polling numbers for the Brexit party – is a more helpful approach. One says: “We won’t get anywhere by simply thinking we are right. We have to understand each other and reach an accommodation so that the terrible prospect of a deregulated, Trump-deal Brexit, that would cost largely Labour voters jobs and a say over their everyday lives, is stopped in its tracks.”

In the end, the dwindling number of rebel MPs, as partly evidenced in that vote on the Letwin amendment came down to two things. First, the Labour operation is incredibly effective – especially since the leadership, a bulk of the PLP, unions and party’s grassroots are all pulling in the same direction. And second, Johnson’s Brexit deal is incredibly awful, particularly on workers’ rights, an issue that is so central to the party. Who needs duct tape when the deal itself will do the work for you?

• Rachel Shabi is a writer and broadcaster