The choice facing MPs on Tuesday – whether to approve the terms of Britain’s exit from the EU negotiated by the prime minister – is the most important postwar decision parliament has confronted. It will irrevocably shape our nation’s future, Britain’s status and influence in the world, our economic competitiveness and the rights of future generations to live, study and work across a continent.

Theresa May’s lose-lose deal looks to be heading for resounding rejection. But there is a risk this will plunge the country into constitutional chaos: a government suspended in place by the Fixed-term Parliaments Act, but unable to offer constructive leadership.

The way out of any such mess lies in the hands of May herself. She must resist the inevitable calls to resign in the wake of a big defeat: to walk away would be a monumental dereliction of duty. Instead, she must lead the country towards the only way out of this gridlock: she must put the deal she has negotiated to the people. The case – and support – for a referendum on Britain’s exit deal has only grown stronger since the Observer first articulated it nearly two years ago. The 2016 referendum result did not create some immutable “will of the people”, a blank cheque for politicians to take Britain out of the EU any which way, regardless of the implications or the cost. The only detailed mandate it provided existed in the fantasies of the leave campaigns: that we could seize back control in a 21st-century, interconnected world, in doing so making ourselves richer and freeing up cash for public services, all the while preserving the sanctity of the union.

A general election, Labour’s preferred route out of the quagmire, would achieve little in moving us forwards

Nothing better illustrates the delusional nature of the promises leavers made to voters than May’s deal. This isn’t some poorly negotiated version of Brexit: it is the best deal she could have achieved given her misconceived red line to end freedom of movement of people while safeguarding peace in Northern Ireland. It embodies the inevitable price for limiting immigration from the rest of the EU (which our ageing population structure anyway dictates we should be encouraging): Britain becoming a rule taker, forfeiting the influential role it has played in shaping EU law, and at great economic cost, to the tune of tens of billions a year. This is the reality that Brexit entails, and voters deserve a say on whether it’s what they want.

On a practical level, there appears no other way forward. The failure of political leadership does not start and end with a prime minister who, a hostage to the Eurosceptic right flank of her party, spent months channelling their claims that there would barely be a price to pay for leaving the EU. Too many MPs – from the hard Brexiters to the Labour leadership – are still living in a fantasy world where the problem is that May just didn’t try hard enough to catch the prized unicorn. So a general election, Labour’s preferred route out of the quagmire, would achieve little in moving us forwards, even if the party could garner the votes to trigger it. There is no apparent parliamentary majority in favour of one single option, not even the so-called “Norway-plus” – vastly inferior to the status quo of remaining.

So voters must be given the chance to endorse May’s deal, or reject it in favour of remaining within the EU. There are no other credible options. Brussels has made clear that the only route to a free trade deal is through the withdrawal agreement, with the backstop as insurance to guarantee an open Irish border, so to put a Canada-style option on the ballot would be to plunge negotiations into chaos. Neither should crashing out with no deal be on it: to offer it would amount to asking the British public if they want to unravel the Good Friday agreement.

The hard Brexiters long ago absorbed the language of populists; even as they warn of the potential for civil unrest in the event of a referendum, they seek to stir it up, accusing MPs of trying to “steal” Brexit from the people. It’s an absurd position: these are the people who wanted to leave the EU so parliament could take back control, but now denounce parliamentarians for thwarting an imaginary, irreversible “will of the people”.

There is no doubt that populists will use a referendum as an opportunity to try to sow further hatred and division. But they must be taken on, not capitulated to. Politicians must not run scared of what’s right, not least because the risk of a populist-cultivated backlash lies at the end of every possible path. Norway-plus – Britain giving up its say over EU law, but still being subject to it – would only give further succour to Eurosceptics. Far from improving people’s prospects, the economic cost of May’s deal would only compound the effects of decades of deindustrialisation and lack of investment in many leave-voting areas of the country.

Those who believe remaining in the EU is the best way of addressing the concerns of many leave voters must make a positive case, which articulates why striving for 19th-century-style national sovereignty is an absurdity in a 21st-century world where the only way to tackle global challenges such as corporate tax avoidance, international crime, terrorism and climate change is through international cooperation. And why staying in would generate a huge dividend that can be spent on improving the NHS and reskilling people who lose their jobs because of technological change.

Given the abject lack of political leadership in Westminster, the people have a right to accept or reject May’s deal. Responsible politicians who care about the national interest will then have the fight of their life to persuade voters that to settle for May’s deal would be to sleepwalk into an act of national self-harm.