The problem with recommending good options for Labour on Brexit, with regards to their electoral prospects, is that none exist. Here is a party whose members and existing voters supported remain, but which cannot win a general election without leave voters. The only six seats lost by Labour in 2017 heavily opted for Brexit in the referendum, such as the ex-mining community of Mansfield and post-industrial Stoke-on-Trent South. And 41 of the top 54 Tory-held target seats – without which Labour cannot form a majority – voted leave. As long as Brexit dominates and defines political debate, Labour will suffer. Its popular domestic policies are sidelined.

Corbynism is an insurgent project, with a clear sense of “the people versus the elite” at its heart; but in order to keep its electoral coalition together, it has been forced to triangulate on the most important political issue of our time, sapping it of the radical energy it thrives on. Brexit has unleashed a culture war, too, which divides and polarises Labour’s electoral coalition.

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Labour is now set to commit to an amendment tabled by backbenchers Peter Kyle and Phil Wilson: which would force a referendum, should Theresa May’s deal pass. There is one minor hiccup with this plan. Unless the parliamentary arithmetic has changed – dramatically so – this amendment will be voted down, decisively so. The vast majority of Tory MPs will vote against, but critically, a significant chunk of Labour MPs – most of whom are far from Corbynites – will refuse to vote for a referendum, however much pressure is put on them. They represent leave seats, endure voters yelling at them on doorsteps that “we voted to leave three years ago, why haven’t we left yet?”, and often made promises to their constituencies at the last election not to stop or reverse Brexit.

Ever since the referendum result upended British politics, it has been claimed by many that Labour is in possession of a big shiny Stop Brexit button that it is spitefully refusing to press. This theory is about to meet its nemesis: political reality. When the amendment falls, there will undoubtedly be relentless attempts to blame Labour, that it didn’t whip hard enough. But such claims will be based in cynicism rather than truth.

Yet there remains a political dilemma for Labour’s leadership. It needs to maintain the support of – and win more – economically leftist leave voters, whose voices are rarely heard on social media, but who are nonetheless numerous. After supporting this referendum it will have to tell them: look, we tried to make this work, we resisted relentless pressure for three years, we even endured a split, but the Tories’ disastrous mismanagement of Brexit left us with no option.

And it is torn in another direction, too. One of the most striking political phenomena of the last three years is that while the “Stop Brexit” campaigns have failed to win over leave voters in any decisive number, they have succeeded in making existing remain voters more angry about Brexit than they were the morning after the referendum result. This should inspire sympathy. The Tories crafted Brexit as an anti-migrant crusade, as well as an attempt to slash and burn workers’ rights and consumer and environmental protections.

This plays perfectly for the new Independent Group. It has no hope of winning a mass following on the basis of its political prospectus, a mishmash of Blairism and socially liberal Thatcherism. Their only hope is to target those remain voters most furious about Brexit – so it has an interest in whipping up this discontent, rather than moving forward from whatever Brexit mess we end up with.

Labour has to lovebomb those remain voters, too, emphasising the political chasm that exists between it and a Tory party increasingly dominated by the Rees-Mogg tendency. The next election, of course, will be a choice between a hard right, hard Brexit Tory party and an anti-austerity Labour party which, at the very least, supports a soft Brexit. But it must avoid an “it’s us or the Tories, so suck it up” strategy: it needs to inspire, not deflate.

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Who knows? Perhaps, in the coming weeks, if Theresa May’s deal continues to be rejected, a referendum may rise from the ashes. It seems unlikely, and its proponents should be careful what they wish for. There are those of us, in good faith, who fear that a second referendum will be infinitely more bitter and vicious than the first, and that – in a polarised electorate – a leave campaign under the slogan of Tell Them Again would triumph.

That’s why settling on a soft Brexit – and shifting the political conversation back to what May described as the “burning injustices” she failed to address – is so appealing. But second-referendum champions should focus on lobbying those Labour MPs who represent leave communities, as well as spending more time winning over leave voters, and less time making existing remain voters more furious.

Labour itself urgently needs a reset button to regain momentum. Any attempt to shift Labour’s domestic agenda rightwards must be resisted. But for a party being torn in every direction – easy answers, there are none.

• Owen Jones is a Guardian columnist