He said in a letter to European Union summit chair Donald Tusk that if Britain didn't leave by the May 23-26 elections, it would have to elect its own European Union lawmakers. May relies on DUP votes to get her legislation passed after she lost her parliamentary majority.
But May's entreaty fell on deaf ears among lawmakers whose support she needs.
"A crash out Brexit would be unthinkable for the peace process, jobs, trade and to the loss of people's rights and quality of life, particularly in border communities".
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.
The wording of the motion that parliament votes on will be subject to amendments, although it is not clear yet what changes lawmakers would seek to make at this stage. The mechanism, known as the backstop, is a safeguard that would keep the United Kingdom in a customs union with the EU until a permanent new trading relationship is in place.
"The legal instrument that we have agreed is an addition to the Withdrawal Agreement".
In the case of no-deal, the UK Government is committed to entering discussions urgently with Brussels and Dublin to agree long-term arrangements.
"The EU can not try to trap the United Kingdom in the backstop indefinitely, and that doing so would be an explicit breach of the legally binding commitments that both sides have agreed", Lidington said.
Lawmakers would then vote on Wednesday or Thursday on whether to postpone Brexit, which might be the only choice at that point. Another Brexiteer, Owen Paterson, tweeted that Cox's opinion made it "brutally clear" that nothing had changed.
Brexiteers in May's party have accused her of surrendering to the European Union and it was not clear if the assurances she agreed would be enough to win over the 116 additional MPs she needs reverse the crushing defeat her deal suffered on January 15.
"Having studied the documents, I would be surprised if they are sufficient to enable the Attorney General to change the central plank of his December legal advice", Starmer said on Twitter. "The government's strategy is now in tatters".
Sterling, which has see-sawed on Brexit news, jumped 0.8 percent to $1.3250 in Asian trade and rallied to the strongest against the euro since mid-2017.
The deadline for the United Kingdom to leave the European Union is fast approaching, and unless British parliamentarians decide otherwise, it remains 29 March 2019.
Mr Barnier told AFP as he arrived at a meeting of European Union ambassadors: "We talked all weekend and now the discussions, the negotiations, are between the Government in London and the Parliament in London".
Some British politicians call this a "Hotel California" Brexit, because, from their perspective, "You can check out anytime you like, but you can never leave". It is what we do with the second chance that counts.
MPs are expected to vote on the deal on Tuesday, with possible further votes on whether to accept a no-deal Brexit or extend Article 50 in order to delay the UK's departure beyond the current March 29 deadline.
Brexit could be reversed if lawmakers reject the government's exit deal, British foreign minister Jeremy Hunt said on Sunday after two major eurosceptic factions in parliament warned that Prime Minister Theresa May was facing a heavy defeat.
U.K. Brexit Secretary Stephen Barclay told the BBC the government was prepared but acknowledged "no-deal is going to be very disruptive for the economy".
Although the 149 margin was reduced from the record 230-vote defeat of the first "meaningful vote" in January, Ms May was left far adrift from a majority with just 17 days to go to the scheduled date of Brexit on March 29.
"Today is our Hotel California moment".