A no-deal Brexit remains the default option if the Parliament doesn't back May's agreement on January 15, even though a majority of lawmakers supported a motion on Tuesday created to reduce the chances of Britain tumbling out of the bloc on 29 March.
Mr Roache said he was glad the PM had "finally picked up the phone" but that her deal was not "good enough".
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And Labour's shadow Brexit secretary Sir Keir Starmer suggested that the continued uncertainty meant an extension of the Article 50 process, delaying the formal date of European Union withdrawal beyond March 29, "may now be inevitable".
Parliament can establish that it wants a no-deal Brexit to be ruled out.
The Scottish Secretary argued a second vote on the May Plan would "crystallise" matters in MPs' minds and afford them the "opportunity to reflect and understand the real alternatives: crashing out of the European Union in 80 days' time or stopping Brexit altogether".
Penistone and Stocksbridge MP Angela Smith fears her party will be punished at the ballot box by voters in the region and slip behind the Tories into second place if Parliament ultimately votes for Brexit to go ahead.
If Prime Minister Theresa May can't win over Brexiteers, she can work on Labour MPs to form a cross-party consensus.
"It could give the winning party a renewed mandate to negotiate a better deal for Britain and secure support for it in Parliament and across the country".More news: Trump spruiks 'crisis' on border, Democrats demand government re-open
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But a Conservative MP who had been expected to reject the deal, George Freeman, said during Thursday's debate that he would now back it "with a heavy heart" because, he said, the prospect of leaving without a deal was "unconscionable".
Under the EU's backstop proposal, Northern Ireland would have stayed in the single market and customs union while the rest of the United Kingdom withdraws, while Mrs May wanted Northern Ireland treated the same as the rest of the UK.
Anything larger than a defeat of about 60 lawmakers when they vote next Tuesday would probably mean the agreement is close to death and the negotiations are in uncharted waters, several European Union officials said.
A no-deal Brexit would be "a disastrous situation in which we move to the most rudimentary terms of trade with our closest partners", Greg Clark told BBC radio.
"The public needs to have the final say on this crucial decision because, in the end, only the people can really sort this out".
"If the government can not pass its most important legislation, then there must be a general election at the earliest opportunity", he said.
Some of Japan's leading companies in Britain have warned that a no-deal Brexit could be a disaster.
The EU may send a letter to May giving further reassurances over the deal before Tuesday's vote but privately neither side believes this will swing it in the government's favor.
An EU diplomat told AFP on Tuesday that "we are convinced that Theresa May will request a postponement after the agreement is rejected in the British parliament".
Britain's de-facto deputy prime minister, David Lidington, said politicians must abandon "fantasies about magical alternative deals that are somehow going to sort of spring out of a cupboard in Brussels".