Despite the changes Theresa May acquired to her deal last night in Strasbourg, the “legal risk” of the UK being trapped in the backstop with no route out “remains unchanged,” according to Attorney General Geoffrey Cox’s legal advice.

Hopes were high that the Prime Minister had done just about enough during her trip to Strasbourg yesterday evening to meet with European Commission President Jean-Claude Juncker, and the EU’s chief Brexit negotiator Michael Barnier. In a statement to the Commons on Monday evening, as the negotiations between May and Juncker were ongoing, David Lidington, May’s de facto deputy, told a packed chamber that the PM had acquired “legally binding” changes to the backstop.

Talk of “legally binding” changes seemed to give members of the government some optimism that May’s deal could pass a vote in the Commons this evening, despite suffering a record-breaking defeat of 230 votes in January. However, since Cox published his legal advice today much of that hope has dissipated.

The point of contention, as ever, is the backstop. Brexiteer MPs fear that the UK could be stuck in the backstop indefinitely with no way out, if no alternative solution to avoiding a hard border in Ireland is found. The final clause of Geoffrey Cox’s legal advice confirms that that is still a real possibility: “The legal risk remains unchanged… if the situation does arise, the UK would have no internationally lawful means of exiting the protocol’s arrangements.”

Addressing the Commons this afternoon, Geoffrey Cox reiterated that the legal risk of being stuck in the backstop remains unchanged. But the agreement from last night strengthens the UK’s case when it comes to negotiating alternatives to the backstop, he said. He emphasised that the situation facing the House now is a political judgement left to MPs. Cox maintained his endorsement of May’s deal.

Shadow solicitor general Nick Thomas-Symonds responded to Cox, saying the final clause of the legal advice “sink” any claim the government can make to a unilateral right to exit the backstop.

Responding to a question from Nigel Dodds, Westminster leader of the DUP, Cox said it would be “unconscionable” for the EU to reject all alternative proposals from the UK to avoid falling into the backstop. If they were to do that, they would be acting in bad faith, he added.

While the legal advice will spook many Brexiteers, the previously anti-deal MPs who are looking for a reason to support May’s deal this time around may have still been given a ladder to climb down. While the technicalities of the agreement have not changed, the EU has strengthened its commitment to prevent the UK from falling into the backstop – a situation which both sides of the negotiations have repeatedly emphasised is not desirable.

The DUP, who prop up May’s government, said they will scrutinise “the text line by line” before deciding whether to support the deal. However the Financial Times reported this afternoon that the DUP will not back the deal. Former Brexit secretary David Davis said he would support the deal if Geoffrey Cox endorsed it. Environment Secretary and Brexiteer Michael Gove told MPs “if you don’t take this prize, there is the real risk you will see a diluted, softer or less palatable Brexit deal.” Anna Soubry of the new Independent Group confirmed that she would not be supporting May’s deal, citing not just the backstop but also the uncertainty it creates for British business as her reasons.

The European Research Group, an influential group of Brexiteer Tory backbenchers, has said their own lawyers are critical of the changes May secured, seeing them as not going far enough to prevent the UK being trapped in the backstop. It is unlikely that we will see many of them change their mind from the last vote. Even if (and it’s a big if) May does secure the support of the DUP, she will still need 106 MPs who previously voted against her to back her this time around.

Despite the high hopes last night, it appears the parliamentary arithmetic still works against her. Cox’s legal advice seals it.

May faces a heavy defeat this evening, but one significantly reduced from last time.

Brexiteers are now facing a different iteration of the choice that has been facing them for a while – this deal, imperfect as it is; crashing out with no deal; or extending Article 50 which could lead to no Brexit at all.