Theresa May arrives in Salzburg at a time when the Brexit negotiations appear to be stalling over the Irish border question and a failure to respond positively to her Chequers proposals, knowing she will only have 10 minutes at the end of dinner to try to lift the mood.

The buildup has not been ideal. On Tuesday night, Michel Barnier, the EU’s chief Brexit negotiator, made it clear that for all the talk of “de-dramatising” the backstop proposal, he is sticking to its fundamental principle that Northern Ireland will have to stay in the European customs union if no acceptable long-term trade deal can be negotiated, and there will have to be what he calls “technical checks and controls” down the Irish Sea.

That, May has said repeatedly, with an eye on her allies in the Democratic Unionist party and the absence of a parliamentary majority, would amount to a compromise of the UK’s territorial integrity that no British prime minister could contemplate.

The message, however, seems not to have got through to the EU27 – leaving No 10 to pin its hopes on the Salzburg summit. The diplomatic aim is for May to make the argument to her counterparts in person in the hope it will percolate and precipitate progress at the next European council meeting in October, after the Conservative party conference.

As for the dinner on Wednesday, the Brussels briefing notes make it clear “the main topic of discussion will be migration”, not Brexit. It may not be until coffee is served that May has her chance to speak, a moment pointedly billed by the European commission as an address and not a discussion where an immediate reaction can be expected.

What she will say was foreshadowed in an op-ed overnight, published not in a British newspaper but Germany’s Die Welt. “To come to a successful conclusion, just as the UK has evolved its position, the EU will need to do the same,” May wrote.

“Neither side can demand the unacceptable of the other, such as an external customs border between different parts of the United Kingdom – which no other country would accept if they were in the same situation.”

The hope is that she can persuade EU leaders to see the issue from her point of view and contemplate, when they return to discuss Brexit over lunch without her on Thursday, that the EU position on the backstop is not one she will be able to sell to her party, parliament or country – however much Barnier and others are focused on the integrity of the single market.

No 10’s second, more political goal is to ensure May’s Chequers proposals for the UK’s future relationship with the EU also receive a hearing. The plan involves a long-term customs relationship with the EU, which would obviate the need for the backstop if it could be agreed and implemented soon after 2019, and includes the UK agreeing to share the a “common rulebook” for food and goods after Brexit, an idea hated by Boris Johnson and hard Brexiters for its perceived curtailing of British sovereignty.

The nightmare scenario is that EU leaders will dismiss Chequers out of hand on Thursday afternoon as Salzburg wraps up, but that is highly unlikely, not least because EU leaders are painfully aware of May’s short-term political pressures. The fear is there will be a critical leak or hostile remark; the hope is there will be some cautiously warm words from key figures at the press conferences that traditionally end these summits.

Neither side expects Salzburg to amount to anything dramatic – the real negotiations will probably run between mid-October and mid-November – meaning every phrase and nuance will be closely scrutinised in an argument about interpretation that will set the tone for the prime minister’s trip to Birmingham in a week and a half’s time.