European officials are pessimistic about the chances of a breakthrough in Brexit talks this week, as negotiators suspect that whatever they offer will not be enough to get the UK parliament to back Theresa May’s deal. According to three people familiar with the situation, there is increasing concern on the European side that any concessions the bloc would be prepared to give would not be sufficient to win a majority in the House of Commons. The EU is reluctant to shift its position if it’s not sure it would get the deal over the line. The view in Brussels is that unrealistic expectations have built up in London, and that attorney general Geoffrey Cox -- sent in by May to negotiate -- is asking for the impossible, according to people briefed on negotiations. EU negotiators are also riled by having to do business with a new interlocutor, the people said. Cox is a veteran barrister known for his ornate rhetoric and a theatrical baritone. Tuesday’s talks were described by European officials as some of the worst-tempered of the two-year process. With just days to go until May has to bring a revised accord back to the parliament that routed her deal in January, positions on both sides are hardening. Each side is counting on the other to back down in a game of brinkmanship. Brexit purists in London, who appeared to be softening toward May’s deal last week, are once again stiffening their resolve. Even as there’s still time for positions to shift, UK officials are mapping out what happens next if her deal is defeated again. Still, the risk of a no-deal Brexit has been taken off the table, at least for now. That is because Parliament has been handed a veto over a chaotic exit, and previous ballots indicate lawmakers would prevent the catastrophe scenario businesses dread. If May’s deal is rejected on Tuesday, Parliament will instead most likely vote to extend the exit day deadline and pro-EU lawmakers will try to force the government to soften, or even reverse the divorce. In a sign of parliamentary compromises that may emerge, opposition Labour Party leader Jeremy Corbyn on Wednesday met for more than an hour with the Conservative former ministers Oliver Letwin and Nick Boles, who support a soft Brexit in an attempt to forge a common approach. That diminished threat of no-deal also eases the pressure on the bloc to make concessions, according to one of the people familiar with the situation. Cox wants the EU to agree to independent arbitration of the contentious Irish backstop arrangement so that it can be ended without needing the consent of the European Court of Justice. The EU says it can’t accept that. The British government agrees that talks were "difficult" but expects them to resume this week, and if there’s progress, May could go to Brussels at the weekend or on Monday. UK officials are concerned that the EU is misreading Westminster dynamics, and have given up May’s chances next week too early. As May’s team contemplates defeat next week, the government is trying to send a clear message to those considering voting down her deal: she doesn’t plan to head back to Brussels to extract new concessions. Instead, Parliament will take control, and MPs who do not like the deal on offer will like the alternative even less.