By BLOOMBERG

LONDON • Prime Minister Theresa May’s chances of getting a Brexit breakthrough this week receded as the Northern Irish ally that props up her government continued to resist a deal amid rumblings of a Cabinet rebellion.

The Democratic Unionist Party (DUP) thinks it will be challenging to get a deal done this week as it’s demanding significant changes to a text on what the Irish border should look like after Brexit, according to a person familiar with the party’s thinking. That risks pushing May beyond the deadline set by the European Union (EU) if it wants divorce talks to move on to trade by year-end.

May’s proposed solution to the impasse — staying close to EU rules after the split — prompted a revolt this week as the highest-profile Brexitbackers, Foreign Secretary Boris Johnson and Environment Secretary Michael Gove, said the clean break they want from Europe could be endangered.

The beleaguered prime minister has just three days to come up with proposals that will satisfy the EU. If there’s no deal this month the chances of a messy Brexit increase and hardliners in the UK will step up their calls to walk away — what businesses have called a catastrophe scenario.

May and DUP leader Arlene Foster spoke yesterday morning for two hours, a conversation a UK official described as constructive. In her first appearance in Parliament since the breakdown of talks on Monday, May expressed confidence that a deal will be done.

“Negotiations are in progress and very good progress has been made in those negotiations,” the premier told lawmakers in Parliament yesterday.

As European Commission President Jean-Claude Juncker said on Monday, “there are still a couple of things that we are negotiating on and he is confident that we will be able to achieve sufficient progress”.

Lawmakers in May’s Conservative Party who support full separation from the EU attempted to put pressure on the prime minister during her weekly questions session. Peter Bone offered to accompany her to Brussels for the next round of negotiations, Jacob Rees-Mogg asked her if her “red lines” were fading to pink, and Bernard Jenkin urged her to focus on free trade deals beyond Europe.

While all were polite, all were reminding May that she faces a revolt if she’s seen to be softening her position.

The Irish border is one of the most sensitive issues holding back Brexit talks — for historic, political and economic reasons. The border now is almost invisible as both countries are in Europe’s single market, but the UK plans to leave the trading bloc in 2019, taking Northern Ireland with it. That means a border will be needed somewhere — either between Ireland and Northern Ireland or between the enclave and mainland Britain.

“We will ensure that there is no hard border between Northern Ireland and the Republic of Ireland,” May said.

“We will do that while we respect the constitutional integrity of the UK and while we respect the internal market and protect the internal market of the UK.”