The polls have barely moved. Not the polls for the general election, but the ones on voting intention in a second referendum. They show a country as sharply divided on the question as last time. Now remain has shaded a few points into the lead – but most polls find “don’t know” stubbornly high. The conventional wisdom in 2016 was that these voters would break for remain in the final days. Conventional wisdom was confounded.

Leaks from the People’s Vote campaign as it has crumbled into infighting show it to be still in thrall to that conventional wisdom – certain that all we have to do is wait, and remain will triumph. Thin on ideas, complacent on strategy, it seems to have little in the way of targets, even the most obvious of all: converting the split electorate into a social majority.

Strategic blunders have characterised the campaign since its inception. The most glaring, and the one now pulling the campaign apart, is that it slips between arguing for a second referendum as a democratic necessity – as a means for popular sanction or rejection of the terms of any deal – and for a second referendum because it is the most expedient route to remaining in the EU.

The chances of a People’s Vote now depend entirely on the complexion of the next government

Really moving the needle on Brexit would require getting wavering leavers on side, but the campaign’s efforts to do so have been minimal: it prefers to inveigh against its pantheon of folk-devils, from Jacob Rees-Mogg and Dominic Cummings to Jeremy Corbyn. Quietly, some of its organisers accept that it has struggled to escape its reputation as an establishment mafia; its prominent organisational caste of washed-up spin doctors, political exiles and job-hungry apparatchiks hasn’t helped. When Boris Johnson’s withdrawal bill looked close to passing last week, it seemed time for the campaign’s last rites to be read. The general election has granted it a reprieve, but one in which its serious options are now few.

It is astonishing that People’s Vote should have squandered its obvious opportunities: it is well funded, operating with resources that would make most single-issue campaigns sick with envy. The campaign has simply failed to learn the lessons of the first referendum. The remain campaign in 2016 had the unenviable task of uniting left and right in defence of a political arrangement they liked for different reasons: the right for the EU’s opening up of markets and liberalisation of economies; the left because of freedom of movement and cultural exchange, and the European court of justice’s tendency to act as a bulwark against the worst excesses of British governments. They settled on an arid defence of technocracy with a healthy dose of fear.

That strategy remains broadly unchanged, though there are other strings to the bow: confronted with a choice between articulating a political argument for a new vote that could bring leavers on board, and exploiting the newfound – if ersatz – enthusiasm for the EU among the remainer base, it has pivoted heavily towards the latter. This is consistent: the groups organising for a People’s Vote have always assumed that to get a referendum means they will win it; that means keeping their base fired-up and intransigent. Remain’s highest-profile campaigners are ebullient partisans in the Brexit culture war, blending seamlessly with the digital fringes of Remainia as they muse about leavers’ relative education levels and the manipulative effects of numbers on the side of buses.

This is not the serious self-examination of a losing side, but the injured outrage of people who believe they ought to have won, marred by snobbery and self-exculpation.

Caroline Lucas has been one of the few remainer politicians to take the loss seriously. Her “Dear Leavers” video campaign recognised the desire to give the establishment a kicking, and tried to understand the vote as motivated by Britain’s astonishing regional inequality, its debased democracy, and the long, slow destruction of its social settlement. The political strategy that might emerge from this excavation would involve more difficult work than the uncritical EU boosterism that’s now in vogue; it would require a relentless accounting of the failures of successive British governments, too often and too easily blamed on Europe.

Green Party MP Caroline Lucas. Photograph: Victoria Jones/PA

Instead, People’s Vote has persisted in the belief that there is a latent majority in Britain for both a second referendum and a vote to remain. In its more grotesque form, this assumes that demographic shift is the agent of change: as older leavers die off, a wave of younger voters will flood to the ballot box to smash Brexit for good. Recent political history is littered with failed progressive movements that pinned their electoral hopes on such shifts.

The strategy is an apolitical one: an unreliable youth wave takes the place of attempts to politically persuade wavering leave voters to change their vote, or think about how the gulf between both poles could be bridged. In an intensely politicised moment, this is insufficient.

MPs affiliated to the People’s Vote campaign also dreamed that such a majority might emerge as an exasperated and deadlocked parliament turned its eyes to a second vote. That dream – never credible against parliamentary arithmetic – is done. The chances of a People’s Vote now depend entirely on the complexion of the next government.

The most notable success of the People’s Vote has been to tar the Labour party with the Brexit brush, and disillusion many of its most ardent remainer voters. It is a rich irony, therefore, that its only hope of success now lies in a Labour government. For all the scorn poured on Jeremy Corbyn by PV functionaries, the Labour party, under his leadership, opposed Theresa May’s deal, and it opposes Johnson’s harder version of the same text. Any future People’s Vote can only be built on Labour foundations.

It is also party policy. Labour’s activist base and its parliamentary cohort is overwhelmingly for remain; it is acutely aware, however, that a sizeable chunk of its voters were for leave. The Labour party has always thought of itself as a party of the whole nation; it is instinctively averse to the Liberal Democrats’ current strategy, which is geared to appeal to an enthused fifth of the country by promising revocation without further democratic exercise. The rollout of dodgy tactical voting sites directing remainers to choose the Lib Dems even in seats where they finished a distant third in 2017 – like the one launched this week by Best for Britain – may end up handing Johnson the Brexit of his dreams by turning Labour-Tory marginals blue.

Labour’s cautious strategy will not always please PVers, who sometimes mirror the ERG’s impatience to “get Brexit done”. But the party is right to intuit that its offer of a second referendum must be presented with a plausible option to leave – with improved guarantees on workers’ rights, watered down in Johnson’s deal – and that Brexit itself should always be considered alongside its wider social and economic programme. Refusing to pretend politics began on 23 June 2016 allows Labour to touch on the deep inequalities and democratic atrophy that churned underneath the Brexit referendum. Reintroducing those questions to Brexit might also provide the People’s Vote with the only means to reach beyond their remainiac base.

People’s Vote has been granted a reprieve. It may be a bitter pill for many of its campaigners to swallow, but the truth is this: the fate of a second referendum now depends on Jeremy Corbyn’s Labour party.

• James Butler is co-founder of Novara Media