If it was the season of peace and goodwill towards all, then politics failed to get the memo. Not only did hostilities continue through the Christmas period, some of the main protagonists announced in advance that they were incapable of taking a break. If anything, the holidays provided more opportunities for irate, booze-fuelled Twitter rants. One particular object of ire was Jeremy Corbyn’s pre-Christmas interview in the Guardian, where he appeared to dash the hopes of many on the left that Labour would immediately become the party of remain.

As the political class sobers up in January and returns to Westminster, it will become apparent that little has changed. The size of the majority against the prime minister’s deal will have diminished but – as No 10 briefed in the run-up to the internal confidence vote in her leadership – it only takes a majority of one. Bizarrely, Downing Street has chosen to amplify the threat of no deal by announcing more money and even the deployment of troops. But this strategy seems set to backfire: it will only give comfort to the European Research Group hardliners that there can be a soft landing to jumping off the cliff edge.

For Labour, it was never likely that Corbyn would announce a decisive shift in position weeks before the meaningful vote and just before the Christmas holidays. Rather, Labour’s position is unaltered from its conference-set policy: its primary objective is to defeat the government on the meaningful vote because the prime minister’s deal has failed Labour’s six tests, which Theresa May herself had promised she would meet. If the government cannot pass its major measure of the day, then a general election is the constitutionally appropriate response.

It makes sense that Labour should seek a general election because its critique of the government goes well beyond the handling of the Brexit negotiations. From an electoral perspective, there are more marginal constituencies that backed remain than marginals that supported leave. It is an open secret in Westminster that a new centrist party is readying to launch and, together with the Liberal Democrats, could form a repository for enough remain protest votes to deny Labour a majority if it were to go into a general election promising to deliver Brexit. It has never been apparent why Labour should fear losing leave voters to the Tories more than losing remain voters to other parties.

While it is true that many Labour constituencies voted to leave, for many of these voters Brexit is a far less important issue than stagnant wages, large class sizes and lengthening NHS waiting times. Moreover, many of these areas are strongly tribally Labour, and what has changed since 2016 is that Brexit is now “owned” by the Tory party. Crudely, many of these voters hate Tories more than they want Brexit. For all these reasons, it is inconceivable that Labour would go into a general election without a promise of a further referendum with a remain option.

The most significant swing voters in a future referendum are working-class women – hit hard by austerity and Brexit is not their top issue

Yet in all likelihood the government would win a confidence vote even if it had lost the vote on the deal. With May’s deal defeated, a general election ruled out, and no deal a calamity, there would be few options left. One option could be for a renegotiation of the political declaration (rather than the withdrawal agreement) but a closer economic partnership would probably see May lose as many Tory MPs as she might be able to persuade opposition MPs.

Even if the political declaration were to be tweaked, it would not be binding on May’s successor—making it politically dangerous for Labour to endorse.

So after the meaningful vote, Labour may be confronted with a choice between no deal and a second referendum. In all likelihood, pro-European MPs will put down an amendment to the finance bill requiring a referendum as a condition of the government collecting tax. Labour may have little option but to back a second referendum if it is to protect the country from no deal which it rightly believes would be a disaster. In this scenario, Labour will want to remind the public that they are being forced to the ballot box again as a result of May’s failure to negotiate a deal that parliament could support, not because of the choices made by the opposition.

That’s why there have been many credible reports of No 10 and Conservative central office ramping up preparations for a second referendum. Paradoxically, it may be that Downing Street is talking up no deal precisely in anticipation of a second referendum – so that it can claim that it was willing to go ahead with no deal but that Labour forced a second referendum. Whatever the manoeuvres, the public are likely to conclude that the government is responsible for the failure of the Brexit project.

With more than 80% of Labour members wanting to remain in the European Union, Labour would plainly back remain in a future referendum. While the remain and leave blocs have proved more resilient than many anticipated, there has been an important shift towards remain, and even more so when offered against the specifics of either May’s deal or no deal rather than the undefined leave option. Corbyn has been repeatedly criticised for his lack of enthusiasm for the EU; but this may prove to be a decisive advantage. It is mildly Eurosceptic voters who need to be persuaded, and Corbyn could speak authentically to this group about the balanced case for voting to stay in the EU.

Crucially, the most significant group of swing voters in a future referendum are working-class women – this group has been hit hard by austerity and Brexit is not their top issue. These are precisely the same voters that Labour needs to win a general election. If Labour’s second referendum message of “vote remain, let’s rebuild Britain instead” can convince them in 2019, it could build the momentum for a Labour victory in the next general election too. And it would smash the generational project of the right, leaving conservatism in disarray.

If there is a second referendum, only Labour can win it – and winning it might be Labour’s path to power. All of this will be determined in the coming weeks. It’s time to take a deep breath.

• Tom Kibasi is director of the Institute for Public Policy Research. He writes in a personal capacity