If a week is a long time in politics, three weeks feels like an eternity in Brexit. Newly installed in No 10 in July, Boris Johnson vowed that he would not sit down for talks with EU leaders until they agreed to drop the Irish backstop from the Brexit withdrawal agreement.

Less than a month later, the prime minister was in Paris and Berlin, where he heard the leaders of France and Germany pledge their support for the “indispensable” backstop – the insurance plan to avoid a hard border on Ireland that has become the stumbling block of Britain’s EU exit.

Johnson said he was “powerfully encouraged” by what he had heard from Angela Merkel, declaring she had set “a blistering timetable” to reach a Brexit deal. Yet Merkel quickly poured cold water over reports that she had set a 3o-day deadline to ditch the backstop. She simply wanted to emphasis that time was short, she said. “It is not about 30 days. The 30 days were meant as an example to highlight the fact that we need to achieve [a solution] in a short time.”

Not for the first time, a British prime minister had misunderstood the German chancellor, who is reputed at home for her sometimes ambiguous statements.

In Paris, Emmanuel Macron sounded cool about finding a backstop alternative in 30 days, but struck a cordial note, saying that said no one was going to wait until 31 October without trying to find a solution.

But behind the politeness and parades, nothing has changed. Merkel and Macron merely differ in style, rather than substance, when it comes to Brexit. The EU has long said it is open to considering “alternative arrangements” to the backstop. But nobody expects them to materialise in 30 days and that is why the EU remains wedded to its Irish insurance plan.

For the EU, the backstop is a guarantee of keeping the peace in Ireland, but also a defence against defective toys, poisonous shrimp or chlorinated chickens finding their way on to the EU’s single market via a UK that will no longer be following EU rules. That is why Macron described the backstop as not just “legal quibbling, but indeed genuine, indispensable guarantees to preserve stability in Ireland [and] to preserve the integrity of the single market which is the foundation of the European project”. The backstop is where the EU’s lofty peace goals and hard economic interests meet.

Meanwhile diplomats have been unimpressed by alternatives proffered by a group led by Greg Hands and Nicky Morgan – the “excellent paper” cited by Boris Johnson as his solution. Others are warmer, but think the alternative arrangements group does not offer answers in the short-term.

Dropping the backstop would also send a disastrous message to the EU’s smaller member states that they don’t count as much as larger countries. It would also suggest Europe can be pushed around by stubborn leaders, not an idea the EU wants to convey in the time of Donald Trump.

Behind the scenes the mood is gloomy. While Johnson’s whistlestop tour was in full swing, one senior EU official commented that a no-deal Brexit is now “the working assumption”. It is a view that has cemented following Johnson’s recent statements.

With 70 days until Brexit, the political schedule and parliamentary arithmetic are seen as working against a rejigged deal with the EU, such as a revision of the non-binding political declaration. These constraints boil down to two numbers: 22 and one.

MPs have only 22 sitting days in parliament until 31 October, according to the Institute for Government, unless they decide to cut short the party conference recess or add extra sessions. And Boris Johnson has a majority of one.

“It is the intersection of the parliamentary arithmetic and the political timetable, and the government’s insistence on [leaving on] 31 October that drives us fastest to no-deal,” one official said.

The Brexit endgame will ultimately play out in London, rather than Paris or Berlin.