With little more than a week to go until the Tory party faithful gather in Birmingham for their annual conference, Salzburg was meant to be a political warm-up lap for Theresa May.

Downing Street hadn’t expected an enthusiastic reception for the Chequers plan from EU leaders but, after a series of cautious interventions from Michel Barnier, the hope was that they would make the political space for her to keep her fractious party on board – leaving the serious haggling for October.

Instead, French president Emmanuel Macron chose the moment to present himself as the champion of EU unity in the face of the populist scourge of Brexit; Donald Tusk said key aspects of her cherished Chequers plan were unworkable; and a clunky intervention on the Irish border, with May comparing the EU’s plan to “carving up” Britain, underlined the gap between the two sides.

With both factions in the Tory civil war crowing over her humiliation, she now faces an acute political challenge.

In theory at least, May has three broad choices, as she scrambles to draft a conference speech that could rally her party behind her.

First, she could yield to the vociferous “chuck Chequers” lobby on the right of her party, and announce that the EU’s intransigence means the deep and special partnership she has long advocated is not negotiable – and instead she will pursue a much looser, Canada-style arrangement.

Henry Newman, director of the Open Europe thinktank and a former adviser to Brexiter Michael Gove, advocated that view on Thursday, saying, “she needs to use this setback to reboot her Brexit policy, open the door back to the whole of her party and try to mend some of the divisions which have opened up since the botched handling of Chequers”.

The European Research Group chair, Jacob Rees-Mogg, said: “I think the government needs to go back to the free trade deal that’s been offered by the EU and consider the ERG’s proposal for the border in Northern Ireland.”

A thinner, Canada-style arrangement would open up its own challenges, because it fails to tackle the border issue and could never win the backing of Labour, but it would at least fit the EU’s existing models.

Secondly, May could pivot in the opposite direction, towards something more like a Norway-style deal in the hope of picking up the backing of more centrist MPs and tackling the EU’s concerns about the integrity of the single market.

Mujtaba Rahman, of political consultancy Eurasia Group, said: “There was always a feeling that the EU had put the UK on a curve, and the curve would lead in the end to a Norway-style agreement.”

Labour’s shadow Brexit secretary, Keir Starmer, argued the dynamic in May’s party makes it all but impossible for her to shift any further in that direction.

“It seems to me she’s got herself into an impossible position now, because having expected this meeting to help her going into conference, it’s hindered her,” he said.

“Any sensible prime minister would try to bridge the gap between her position and the EU’s but she’s prevented from doing that by her own right wing. It’s the ERG tail wagging the dog.”

May’s third choice, which she was already rehearsing in Thursday’s awkward press conference, is to brush off the downbeat words of her EU counterparts in Salzburg as a negotiating tactic – and cling on to Chequers.

Both sides have now tacitly accepted that the political declaration that will accompany the withdrawal agreement between Britain and the EU will be a broad-brush document, that could encompass a range of final outcomes.

One Whitehall source said “the political declaration can be all things to all people”. Philip Hammond recently called the document a “heads of terms”; and both leavers and remainers in Westminster are beginning to understand that, to some extent, the real battle about Brexit can be delayed until after the end of March next year.

That means from the EU27’s perspective, Brexit doesn’t stand or fall over the acceptability of Chequers – it’s the backstop for Northern Ireland that is crucially important; and where May’s intransigent language appears to have riled her partners.

Solving the Irish conundrum is tough enough in itself. May’s reliance on the Democratic Unionist party for a majority, and her personal conviction that she must not sign up to anything that could threaten the union, makes her reluctant to compromise. But it doesn’t necessarily demand that she “chuck Chequers”.

Politically though, May is personally associated with the complex edifice of the Chequers deal, for which she lost two cabinet ministers. She will have to tell her party where she stands.

Tory activists were already intensely sceptical about the Chequers agreement, which they fear will bind Britain too closely to EU rules and regulations, and risk fuelling a betrayal narrative among Leave voters.

For those Brexiters who swallowed the plan and remained inside the Cabinet room, the key selling point was that it could form the basis of something the EU27 could accept. That argument now looks hard to sustain.

As May returned to London to lick her wounds, there is precious little love lost for her on either wing of her deeply troubled party – and it is far from clear that she will be given much more time to try to clinch a deal.

Tory remainer rebel Anna Soubry said: “My constituents, 52% of whom voted leave, are fed up to the back teeth of this. What they want is for politicians to lead and guide them, and that is what has fundamentally been missing.”