Theresa May is engaged in a race against the clock to find the key to break deadlock in Brexit talks.
The Prime Minister's hopes of securing agreement on the terms of Britain's EU withdrawal were dashed on Monday when the Democratic Unionist Party refused to accept proposals which would have shifted Northern Ireland's customs border to the Irish Sea.
Mrs May is planning to return to Brussels before the end of the week, with time running out to persuade leaders of the remaining 27 EU nations at a summit on December 14-15 that "sufficient progress" has been made on divorce issues to move Brexit negotiations on to their second phase.
This will deal with trade and the transition to a new relationship.
On Tuesday she was expected to speak by phone with DUP leader Arlene Foster as she grapples to find a form of words acceptable to the Northern Irish party, on which she relies to prop up her minority administration at Westminster.
Mrs May had to break off from talks with European Commission president Jean-Claude Juncker on Monday for an urgent call with the DUP leader, after she dramatically declared her party's implacable opposition to proposals which would have imposed "regulatory alignment" between Northern Ireland and the Republic in order to avoid the need for a hard border.
Irish premier Leo Varadkar said that the deal had been agreed by the European Commission, UK and the Republic before the process was thrown into disarray by Mrs Foster's eleventh-hour intervention. He said he was "surprised and disappointed" by Mrs May's request for more time.