The main sticking point in Brexit talks is agreeing on a legally binding "backstop" arrangement to keep open the border between British-ruled Northern Ireland and the Republic of Ireland, an European Union member state, whatever the outcome of future trade talks.
"First, the European Union says there is no time to work out the detail of this UK-wide solution in the next few weeks, so even with the progress we have made, the European Union still requires a backstop to the backstop - effectively an insurance policy for the insurance policy".
Mrs May will address the leaders of the remaining 27 European Union nations tomorrow before they discuss over dinner without her how to proceed in the talks.
The weekend was meant to be a chance to crack the thorniest issue in talks - what to do with the Irish border - so that leaders meeting for a summit on Wednesday could declare progress and signal that a final deal could be signed in mid-November.
Theresa May has given her strongest indication to date that MPs could be given the chance to block the United Kingdom leaving the European Union without a deal.
Writing in today's Irish News, deputy leader Ms O'Neill accused the unionist party of pursuing a "reckless agenda". And with the clock ticking, Sterling remains under downside pressure as odds of a no-deal Brexit tick higher.
The DUP leader said that nobody wants to see physical infrastructure on Irish border and expressed hope a sensible Brexit deal can be achieved. An EU official said no further negotiations were planned before the leaders of EU countries convene in Brussels.
"Nobody wants to ever trigger the backstop, but it needs to be there as an insurance mechanism to calm nerves that we're not going to see physical border infrastructure re-emerging", Coveney said.
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This year, the government suggested Britain could apply the EU's external tariffs for a limited period in case of any delay in implementing a Brexit deal.
On Sunday, former Brexit Secretary David Davies urged Cabinet members to rebel against Ms.
But they were disappointed by the issue that has dogged the talks for months - how to ensure that no hard border is created between the EU's Ireland and Britain's Northern Ireland once Brexit happens on March 29.
Following three days of talks with key figures in Brussels, DUP leader Arlene Foster said the Prime Minister could not in "good conscience" accept the proposals now on the table from the EU.
But Brussels had said there was not time to work out the details, she said, and proposed its own fall-back plan - the "backstop" - that would see only Northern Ireland align with European Union rules.
The Northern Ireland "backstop" has emerged as the main stumbling block in the Brexit negotiations.
It opposes any new checks on goods between Northern Ireland and Great Britain and has threatened to pull support from the government over the backstop issue.
Britain only wants it in place for a limited time, but Coveney said that "a backstop can not be time limited".
"The people have already voted on Brexit", the PM told the Parliament.
Brexit supporters accept there is likely to be some short-term economic pain but say the government is trying to scare voters about the impact of a no-deal exit.