However, when the BBC asked what happens if the deal is defeated, Barclay said he suspected the Commons would support something "along the lines of this deal" but did not speculate on whether the government had a Brexit "plan B" lined up.
A failure to deliver Brexit would be "a catastrophic and unforgivable breach of trust in our democracy", Prime Minister Theresa May has warned.
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Dominic Grieve has urged the Prime Minister to delay Brexit in the likely case that her withdrawal agreement is rejected by MPs next week.
"If the UK is a genuine partnership of nations it is essential that the views of the people of Scotland, the Scottish Parliament and Scottish Government are taken seriously, and not ignored, when the vote on the UK Government's deal takes place on Tuesday".
Jeremy Corbyn has dashed hopes he could back a so-called "People's Vote" by saying he wants a renegotiated Brexit deal.
Corbyn said: "I think parliament did vote for an amendment to the Finance Bill this week, which indicated its opposition to no deal, but it isn't totally specific on it".
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He used an article in the Sunday Telegraph to urge MPs to vote down Mrs May's "bad" deal to send a message to Brussels that the United Kingdom "will not be bullied".
Dominic Grieve, the former attorney general, suggested the March 29 exit date should be removed from domestic legislation if the prime minister's Brexit deal is defeated, before the United Kingdom goes to the European Union to ask for an extension to Article 50.
"The UK Government's Brexit deal will take Scotland out of the European Union against our will".
Mr Hunt warned: "If we were, as a political class, not to deliver Brexit, that would be a fundamental breach of trust between the people and the politicians. We will do everything we can to prevent a no deal exit".
This will be a crucial week for the future of Scotland, but I urge MPs not to think just of the days to come but of the generations to come.
It would see the United Kingdom keep the Withdrawal Agreement thrashed out by the prime minister with Brussels, but significantly rewrite the Political Declaration to state an intention to stay in the single market.
The PM has also faced further opposition to her deal from former Brexit secretary Dominic Raab, who used an article in the Sunday Telegraph to urge MPs to vote down Mrs May's "bad" deal and send a message to Brussels that the United Kingdom "will not be bullied".