If shambolic government turned leavers into remainers, Britain would have decided long ago not to bother with Brexit. But that isn’t how it works. The sight of Theresa May failing to organise a departure from the EU proves that she is unequal to the task, not necessarily that the task should be abandoned. For many Eurosceptics, it has the opposite effect. They see the fact that Brexit has broken a stolid prime minister as confirmation that gung-ho leadership is the missing ingredient.

The same applies with deadlock and procedural mayhem in parliament. Pro-Europeans cheer when a majority of MPs vote that the country should not be yanked out of the EU without a deal. They salute the Speaker of the House John Bercow when he uses ancient protocol as a bat, thwacking May’s twice-rejected withdrawal agreement out of the Commons chamber without another vote. In the eyes of a remainer, this is the legislature defying of bad government; democracy in action. The leaver sees rogue lawmakers obstructing the popular will; democracy betrayed. Few minds are being changed.

We are edging away from the EU exit, but not towards resolution of the social and political tensions exposed by the referendum. This is a dangerous dynamic. The remain cause makes tactical progress, helped by the ineptitude of its enemies, but the argument for being part of a European project has barely advanced. If Britain wants to preserve a healthy relationship with its nearest allies, it is not enough that Brexit fails. More people must want it to fail.

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Opinion polls suggest a steady tilt towards remain since 2016, but the lead is not bigger than the volume who aren’t sure either way. A niggling feeling that the wrong fork was taken on a road three years ago is not a guaranteed vote to turn back. It depends how the question is framed and why it is being asked.

There is one kind of referendum that could be seen emerging from grassroots demand and as a necessary antidote to deadlock and confusion. It could be won by pro-Europeans in optimistic spirit campaigning for a forward-looking country, more at ease with its neighbours and itself. But there is another referendum, born from desperation in an extended article 50 negotiation and portrayed as arrogant Brussels demanding a different answer to the same old question. In that contest, a campaign urging Britain to stick to its Eurosceptic guns would be hard to beat.

If public opinion is fluid, positions inside parliament are hardening. At the start of the week there was chatter about Tory hardliners shifting towards support for May’s deal. There is always the prospect of a Treasury cheque big enough to remind the DUP how much they support the government. But such movements do not indicate sincere softening. There are no MPs who thought the deal was bad in January but now think it is good. The likes of Boris Johnson and Dominic Raab would never support May’s version of Brexit if they thought it would be the final settlement. Their calculation is that the prime minister will be defenestrated before too long. The Tories will then need a new leader who (the candidates imagine) can rip up his predecessor’s legacy.

In reality, Britain would enter new circles of hell trying to wriggle out of signed and sealed withdrawal treaties. That is no deterrent to Johnson, Raab, David Davis and others. They have already seen at close quarters what is possible in a negotiation with the EU and still embraced the opposite. They have cynical and ideological motives to lend May just enough support to finish the job of killing EU membership. Those incentives get stronger as the prospect of Brexit being delayed, or even abandoned, grows.

Facebook Twitter Pinterest ‘The people’s vote campaign often gets the argument about how to keep EU membership and whether to do it the wrong way round.’ Photograph: Tolga Akmen/AFP/Getty Images

Leavers’ growing fear of losing Brexit is not matched by remainers growing more confident in the case for EU membership. Pro-European MPs focus on May’s deficiencies. Then they argue that a final decision should rest with the people. But a referendum is a procedure not an outcome. When someone calls for one it is never a secret what result they prefer. Only in the Commons are people who hate Brexit so squeamish about getting to the point of saying it should be stopped.

Much of that awkwardness is a function of Labour contortions. The party has a notional pro-referendum policy but a bunch of the party’s MPs hate the idea and its leader struggles to endorse it. There is a difference between a policy that Jeremy Corbyn accepts and a cause for which he campaigns. He lambasts Tory handling of Brexit in his loudhailer voice, but is all diffident mumbles on the question of whether Brexit itself is a good idea. Even if circumstances conspire to deliver a plebiscite, Corbyn will not make a passionate advocate for EU membership because he doesn’t like it.

Corbyn has a managerial dilemma. It is tricky being the Eurosceptic leader of a pro-European party. But there are MPs who do believe that Britain is better off as an EU member and yet still struggle to say so aloud. They would rather wait until there is no question left to ask except the one that really matters. Should we call it off? But the longer remainers hold out for that moment, the harder it gets to pull their reasons out of procedural weeds and party political sludge. There is a danger that Britain gets bogged down in an article 50 extension and when the campaign engines rev up to take us into reverse, the wheels will spin without traction.

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The people’s vote campaign often gets the argument about how to keep EU membership and whether to do so the wrong way round. Anyone who wants a second poll already hates Brexit. People who liked Brexit in 2016 but think it might have gone sour need something more positive to believe in than parliamentary process and referendums. The pitch has to open with the image of a happier, confident Britain, relieved of the grinding burden of endless Brexit bickering, taking its rightful seat at the top table of continental power, ready to lead. If enough people think that is the country we want to be, the case for a public vote makes itself as the way to get there.

That doesn’t mean everyone should learn the Ode to Joy and paint their face blue. It does mean that remainers must challenge the conventional wisdom that British voters are culturally immune to pro-EU arguments. There are too many MPs waiting for the architects of Brexit to soil themselves so thoroughly in absurdity and paranoia that their cause is ruined and their ideas discredited forever. But the humbling of leavers and the obstruction of their plans is not all good for remain. Not if it can be cast as the work of a conspiracy by Brussels, Whitehall and parliament.

Extension to the article 50 period is the most probable next move, which looks like a tactical gain for pro-Europeans. But engineering a situation where Britain’s EU membership survives beyond the original 29 March deadline was the easy part. The hard bit is making it look like a victory for common sense, not a defeat for national pride. Otherwise a setback for leave is no advance for remain. The crisis in British politics is severe enough that both sides can be losing at the same time.

• Rafael Behr is a Guardian columnist