Theresa May's chances of getting a Brexit breakthrough in the coming days hinge on the prime minister convincing the Northern Ireland party that props up her government to accept the U.K. position on the Irish border.

The frontier between the north and south of Ireland has emerged as the biggest threat to getting a deal next month that would allow the U.K. and European Union to start discussions on future trade, three people familiar with the discussions said on condition of anonymity.

E.U. chiefs are expecting May to offer more money toward liabilities such as pension promises and infrastructure projects it had committed to but has yet to pay. But a disagreement with the Democratic Unionists over how far she can go on the border question could scupper the deal.

Irish and E.U. officials have suggested that Northern Ireland be given a different status to the rest of the U.K., implying the creation of a border between Northern Ireland and the rest of the U.K., but the DUP is adamant that can't happen.

"We need more clarity and more certainty around a road map to deal with the border issue comprehensively," Irish Foreign Minister Simon Coveney said in an interview with Ireland's RTE radio on Monday. If businesses in Ireland and Northern Ireland are operating under different rules, "it seems impossible to us that you avoid a checking system and therefore some form of hard border."

Ireland has the backing of the rest of the E.U. in wanting written assurances that the U.K.'s withdrawal from the bloc's customs union and single market won't lead to a return of checkpoints that would stir memories of violence between Catholic and Protestant groups.

The U.K. side doesn't want a hard border either but insists a solution to the problem can emerge only in conjunction with a final trade deal. May had hoped to park the issue, but it's become a red line for the Irish — whose government has dug in while it faces down its own political crisis in Dublin.

The whole thing is complicated by the fact that May relies on the support of the pro-Brexit DUP — a party rooted in Protestant support for Northern Ireland's place in the U.K. — after losing her parliamentary majority in June's election.

On the other hand, it's not clear exactly how far the DUP would go toward blocking any possible wording as it might be wary of bringing down May and opening the door for a Jeremy Corbyn-led government. The DUP has been heavily critical of the leader of the main opposition Labour Party currently ahead in opinion polls.

"The island of Ireland is now faced with many challenges," the E.U.'s chief Brexit negotiator, Michel Barnier, said in a speech in Brussels last week. "Those who wanted Brexit must offer solutions."

Officials from the E.U. and the U.K. continued discussions in the past few days in a push to reach a joint position on the most pressing Brexit issues that must be solved before talks can advance, the people familiar with the discussions said.

A written offer on the financial settlement has already been drafted pending May's final approval, one of them said. May's spokesman dismissed that on Monday as speculation.