May, who faces one of her most crucial weeks since becoming prime minister, will address the backbench Conservative 1922 Committee on Monday evening to tell her MPs that, even though the EU Withdrawal Bill is a largely technical matter, the way they vote will send out a highly important signal to the country.
Parliament will also debate other amendments handed down by the House of Lords, including a challenge to the government's plan to put March 29, 2019, or "Brexit Day", into law and an attempt to toughen a commitment to ensure a frictionless border between Northern Ireland and the neighbouring Irish Republic, which will remain in the EU.
Pro-EU Tories have backed off amid fears Mrs May could be fatally damaged by defeat, opening the way for a hardline Brexiteer to take over at the top of the party.
There are two amendments that could prove particularly tough for the government to overturn.
If she is defeated in the House of Commons, it will be yet another blow to a prime minister whose authority has been challenged several times since she lost the Conservative Party's majority in an ill-judged election a year ago.
"But the message we send to the country through our votes this week is important". I am confident I can get a deal that allows us to strike our own trade deals while having a border with the European Union which is as frictionless as possible. On Wednesday, it will debate an amendment instructing the government to negotiate a customs union with the EU.
Labour and Conservative MPs are bitterly split over Prime Minister Theresa May's desire to keep Britain in the European Economic Area.
Writing in the Scotsman, Mr Murray said it was "deeply troubling" that the Labour front bench was refusing to support membership of the EEA and warned future generations would "ask us why we failed to act".
The Edinburgh South MP added that he was "confident we can smooth some of the particularly rough edges" of the Withdrawal Bill, and said he believed there were enough Conservative rebels to keep the United Kingdom in the customs union.
He has also urged Conservative pro-Remain MPs to "change the course of Brexit" and vote accordingly on a series of upcoming crunch votes in the lower house of parliament.
"The government's position isn't a position, its a sham to get through the next 48 hours and keep Jacob Rees-Mogg in check".
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