"And it makes a legal commitment that the United Kingdom and the European Union will begin work immediately to replace the backstop with alternative arrangements by the end of December 2020".
"There will be no third chance".
Mr Lidington told MPs in a late night sitting in the Commons that the PM had secured legally binding changes that "strengthened and improved" the withdrawal agreement. "We will stand by Ireland & the need to safeguard the Good Friday Agreement", he said, referring to the 1998 peace deal for Northern Ireland.
However, according to a timetable pledged by Theresa May last month, if the latest vote on her Brexit agreement fails to go her way, then the Commons will get a chance to vote on leaving the European Union without a deal - a scenario which has very little support within the UK Parliament.
A deadlock in talks in Brussels on a key provision in the European Union withdrawal agreement is expected to lead to another defeat for Prime Minister Theresa May when the motion on her Plan B is introduced in the House of Commons on Tuesday.
"May has two strategies: threaten no Brexit, and threaten no deal", said Benjamin Martill, a Dahrendorf Forum researcher at the London School of Economics who studies UK-EU relations.
But if they reject it, MPs could vote on Thursday to delay Brexit - giving further time for pro-Europeans to try to undermine the whole process.
"We will certainly analyse that very, very carefully", said Nigel Dodds of Northern Ireland's Democratic Unionist Party (DUP), part of May's coalition government.
The House of Commons overwhelmingly rejected the deal in January, primarily because of concerns over arrangements for the Irish border.
But Slack said the vote "will take place tomorrow". "If she won't find a way forward, Parliament has a responsibility to do so instead", Cooper said.
The deal was struck over more than a year of tough negotiations, and covers Britain's financial settlement, expatriate rights, the Irish border and plans for a transition period. She survived a bid to oust her through a no-confidence vote in December.
European officials said there had been no breakthrough in talks over the weekend and expressed frustration with May's attempts to secure concessions just weeks before Britain's exit.
The Prime Minister has apparently acquired "a joint legally-binding instrument" on the withdrawal agreement.
He warned that UK MPs now needed to back the deal.
If her deal is defeated, May has said she will give lawmakers a vote on Wednesday on leaving without a deal on March 29.
But the details of it were a sticking point for many MPs when they voted her deal down in January.
Any postponement would have to be approved by the leaders of the other 27 nations, who are next meeting at a Brussel's summit on March 21 and 22 - a week before Brexit day.
However, "Parliament could choose to hold another vote of no confidence in her government, which they did after the last meaningful vote", said Maddy Thimont Jack, a researcher at the Institute for Government in London.