In a jam like this, when parliamentary discipline has broken down, No 10 has two last-ditch tactics up its sleeve. The first is to try to pull off the psychological trick of persuading MPs that the mood is changing, and that they had better fall in line before they miss the bus. The second is to blackmail them by painting a picture of how awful the alternative to the prime minister’s deal is, underlining that the responsibility for the ensuing chaos will lie with MPs who vote against her.

Unfortunately for Theresa May, neither of these ruses is likely to work this time. No 10 has been briefing since before Christmas that it is making progress with the European Union on the backstop and will soon be able to unveil changes that will make the plan acceptable to the rebels. Downing St also says it is in talks with the Democratic Unionist party – and if the DUP changes position on her deal, so will most pro-Brexit Tory rebels. This is either whistling in the wind or, more likely, deliberately misleading.

The DUP’s demands that the backstop be made time limited, or that the UK should be able to end it unilaterally, are impossible because they defy logic. The backstop cannot be time limited exactly because it is a backstop. Any end to the backstop needs to be conditions-based, not time-based, when an alternative way has been found to preserve the open border between Northern Ireland and the rest of Ireland. Despite two years of looking, neither the government nor the Brexiteers have found an even remotely satisfactory alternative. This means that it is impossible to amend the backstop as the DUP wants, without destroying it, even if Brussels were willing to do so. So the best that May can hope for is some warm words from an anxious-to-help Brussels suggesting the EU does not want the backstop to be permanent.

The prime minister may hope this will somehow be enough to persuade the DUP to change its position and support her. In my experience of dealing with the DUP over many years, she is likely to be disappointed. When its leaders say something, it should be taken literally. Getting them to back down is usually not an option, as she discovered to her cost a year ago.

Quick Guide Brexit and backstops: an explainer Show A backstop is required to ensure there is no hard border in Ireland if a comprehensive free trade deal cannot be signed before the end of 2020. Theresa May has proposed to the EU that the whole of the UK would remain in the customs union after Brexit, but Brussels has said it needs more time to evaluate the proposal. As a result, the EU insists on having its own backstop - the backstop to the backstop - which would mean Northern Ireland would remain in the single market and customs union in the absence of a free trade deal, prompting fierce objections from Conservative hard Brexiters and the DUP, which props up her government. That prompted May to propose a country-wide alternative in which the whole of the UK would remain in parts of the customs union after Brexit. “The EU still requires a ‘backstop to the backstop’ – effectively an insurance policy for the insurance policy. And they want this to be the Northern Ireland-only solution that they had previously proposed,” May told MPs. Raising the stakes, the prime minister said the EU’s insistence amounted to a threat to the constitution of the UK: “We have been clear that we cannot agree to anything that threatens the integrity of our United Kingdom,” she added.

So she has little chance of persuading the DUP – and by extension the mass of Brexiteer Tory MPs – to back her deal. That leaves her with the final tool, of blackmail. The reason why the government is now upping the rhetoric on how awful a no-deal Brexit will be is perfectly transparent. No deal is no longer better than a bad deal: it is her deal or Armageddon. And she wants to make MPs believe that if they vote her deal down, they will be held personally responsible by their constituents for the impact on voters’ lives.

I find this threat entirely incredible. The reason why a no-deal Brexit is not going to happen has nothing to do with there being a majority in parliament against it. Parliament has no say in stopping the inexorable progress of article 50, which will take us out of the EU at the end of March this year.

Rather, it is the instinct for self-preservation that will make the government pull the emergency brake in the end and ask Brussels for more time – as it can do at any moment up until the end of March. It will do so because is knows how grave the impact would be on day-to-day life in Britain, and it knows that the people will blame No 10 for the chaos – not Brussels or rebel backbench MPs.

If there remain those in No 10 who do not know this to be true, they can take it from me: I lived through the fuel crisis in 2000, when tanker drivers blockaded the fuel depots and we came within hours of having to invoke emergency powers to keep hospitals operating and money in cash machines. Labour’s opinion poll ratings fell through the floor, and we trailed substantially behind the Tories for the first and only time.

Luckily we broke the blockade quickly, but I learned that there is one thing the public expects above all else, and that is that the government governs. That is its job, and it is why people elect it. If it presides over chaos, as Edward Heath did with the three-day week, the government will be out on its ear in short order. May will not want to risk that ignominious fate.

Neither happy talk about imminent breakthroughs nor blackmail will save May’s deal. Once again, the government is wasting time on delusions. The only way out of this mess is for the government to reach for the emergency brake and ask the EU to extend article 50. The sooner it does so, the better.

• Jonathan Powell was chief of staff to Tony Blair from 1995 to 2007