The EU will not budge on the backstop, and that means either Parliament will have to accept the previous agreement with the EU, vote for a no-deal exit, or delay Brexit for more negotiations.
Unconfirmed reports say Theresa May will travel to Strasbourg later.
The vote will be on a statement saying that parliament approves a two-part deal: a legal withdrawal treaty, and a political declaration on future relations with the EU.
When May's deal was first put to the House of Commons in January, more than one-third of her Conservative MPs - 118 out of 306 - joined opposition parties to vote against it. It is due to be published later Monday.
May has promised Britain will leave the European Union whatever happens on March 29, but many MPs fear that a "no deal" exit would wreak economic havoc.
"This evening in Strasbourg the prime minister". Even her many detractors in the party have been reluctant to dump her in the midst of Brexit negotiations.
'I think it would be very hard for the prime minister to stay in office for very much longer, ' she told BBC Radio 4's The World This Weekend.
If the European Union failed to try to find an alternative to the backstop, Lidington said Britain could use this joint instrument "as the basis for a formal dispute through independent arbitration", and ultimately get the backstop suspended.
Finally, the document would put assurances European Union leaders about the temporary nature of the backstop "onto a legally binding footing", Lidington said.
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The main sticking point is a measure to ensure the border between Northern Ireland and Ireland remains open, a key issue for Varadkar's government.
May is hoping for a different outcome to the historic defeat her last divorce deal suffered in January. If that option is voted down as well, the legislature will consider extending the Brexit deadline, now set for 29 March.
Mr Lidington said the Attorney General would be publishing advice ahead of Tuesday's debate, but needed time to consider the new changes.
All EU member states have to agree to an extension, and some EU leaders have expressed concern that it needs to have a specific objective.
"We are committed to using our best endeavours to find a subsequent agreement that replaces the backstop".
Lawmakers are expected to try and make changes to the text of the statement to show that there is majority support for an alternative course of action or to make backing the deal conditional on something such as a second referendum.
"The EU will continue working intensively over the coming days to ensure that the United Kingdom leaves the EU with an agreement". "Let's bring the UK'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.
Brexit minister Robin Walker has been updating MPs in response to an urgent question from Labour.
Nigel Dodds, deputy leader of the Democratic Unionist Party (DUP) which props up May's minority government, and Steve Baker, a leading figure in the large euroskeptic faction of her Conservative Party, said she was heading for defeat. If that falls, lawmakers could then vote on Thursday on a short delay to Brexit.
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Most adults need roughly seven to nine hours of sleep , but everyone's "magic number" that makes them feel well-rested varies. This is a second try for the Florida Republican, who didn't get the time of day from his colleagues in the previous Congress.