Lawmakers are expected to reject that proposition, a day after they overwhelmingly voted against Prime Minister Theresa May's divorce agreement for a second time.
But May's entreaty fell on deaf ears among lawmakers whose support she needs.
That requirement has been rejected previously by London and would be particularly unpalatable to Northern Ireland's Democratic Unionist Party, which props up May's government in parliament and opposes any proposals for Northern Ireland to have different rules from the rest of the United Kingdom. "Let s bring the United Kingdom s withdrawal to an orderly end", the former Luxembourg premier told reporters, sitting next to May at a late-night press conference in the French city.
"In light of our own legal analysis and others, we do not recommend accepting the government's motion today", group member Bill Cash said.
The DUP has pledged to carefully analyse the Brexit deal add-ons, remaining non-committal on whether it would now back the Withdrawal Agreement.
"The legal instrument that we have agreed is an addition to the Withdrawal Agreement".
Lidington said lawmakers faced "a fundamental choice.to vote for the improved deal or to plunge this country into a political crisis".
Theresa May's government has been seeking changes since her negotiated deal suffered a historic defeat in January, but the European Union refuses to reopen the agreement after long negotiations.
Brexit-supporting lawmakers in May's party had accused her of botching the negotiations with Brussels and surrendering on the detail of the backstop which sets out what happens to the Irish border if the sides fail to find a solution.
Senior Conservative MPs urge May to delay Tuesday vote on Brexit deal: Reports
Labour leader Jeremy Corbyn told the House of Commons on Monday that "not been a single change" had been made to the agreement since it was heavily defeated by MPs in January and it was still a "bad deal". "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. May's deal and a no-deal departure.
It comes amid reports Mrs May will fly to Strasbourg, France in the coming hours in a last-minute bid to save her foundering Brexit divorce deal before it is voted on again on Tuesday local time (Wednesday morning AEST).
German EU affairs minister Michael Roth, called it "a far-reaching compromise". "There is no alternative".
But despite the war of words, both sides say talks are continuing over the weekend, just days before May will face parliament once again after resoundingly losing the first vote in parliament on January 15. It is what you do with this second chance that counts.
"Let's do what is necessary for MPs (members of parliament) to back the deal on Tuesday".
UK MPs will today vote on whether to take the threat of a "no-deal" Brexit off the table - by voting for a motion which states that that the House of Commons "declines to approve" leaving the European Union without a withdrawal agreement and framework for a future relationship on March 29th.
Even if the deal is approved, Brexit Secretary Stephen Barclay said there might need to be a "technical extension" so that all the needed laws can be passed. They are likely to agree, as long as Britain leaves before elections to the European parliament in late May. If the option of a no-deal Brexit is not accepted by MPs, there will be a further vote on Thursday on a potential extension of Article 50. "If we don't check out tonight, we may never leave", tweeted Conservative legislator Bob Seely.
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