"The real question for Members of Parliament who voted to give the public a say through the European referendum in 2016, who voted in large numbers to trigger Article 50, is the effect of triggering Article 50 is you either have a deal and the EU have been clear that the only deal on the table is the PM's deal".
MPs will resume debate on the Brexit deal on Wednesday ahead of a vote the following week.
It is the latest in a string of bad headlines for the government over its post-Brexit planning, after it awarded a contract to run freight ferry services from Ramsgate to a company that does not own any ferries.
"The deal that is on the table is the best and the only deal possible", chief spokesman Margaritis Schinas told reporters when asked about a phone conversation on Friday between May and Commission President Jean-Claude Juncker."This deal will not be renegotiated".
Mrs Cooper said that a no-deal Brexit posed risks to the British economy and security that were "far too high" which would be "irresponsible" if allowed to happen.
The DUP - which Mrs May's Conservative Party relies on for a majority in Parliament - has said it will not back the deal.
"We will not be leaving with no deal", he said.
MPs will seek to turn the screw on ministers with Tuesday's amendment, which is meant to demonstrate to the government the strength of opposition to a no-deal Brexit in the Commons.
However, there are those who favour a No Deal Brexit and claim this would be inline with what people voted for in the referendum.
May suffered a fresh blow on Friday when a survey showed most rank-and-file members of her Conservative Party oppose her Brexit deal and would prefer to leave the European Union without one.
May did not respond to an urgent question tabled by Labour leader Jeremy Corbyn "on progress made in achieving legal changes to the European Union withdrawal agreement and the timetable in this House for the meaningful vote", but is due to face him during Prime Minister's Question Time on Wednesday.
The government will on Tuesday launch a new radio and social media advertising campaign created to prepare Britons for the full impact of no deal.
The exercise, known as Operation Brock, is turning the Manston Airport site into a mass holding bay for heavy goods trucks, to ease congestion on major highways to British ports such as Dover, southern England. Now around 10,000 heavy goods vehicles arrive every day at the port.
But as the expectation persists that MPs will reject the May Brexit Plan next week, Whitehall sources admitted senior ministers were as much in the dark about any Plan B as the public was.
Brexit-backing MPs in her Conservative party are still in open revolt while opposition Labour leaders are angling for new elections.
When pressed on the issue during a briefing with journalists on Monday, a spokesman for Number 10 said: "What we are committed to doing is ensuring the statute book is ready for exit day and we will do whatever is required to deliver that".
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