At Westminster, speculation has centred on the prospect of the Prime Minister watering down her commitment to hold a vote on her Brexit deal following the failure of talks to provide suitable concessions over the Northern Ireland backstop.
"It doesn't mean that a public vote has gone, it doesn't mean we won't come to it, but it means Tuesday is about exposing the weakness of the Prime Minister", he said.
Lidington said the sides had agreed a joint legally binding instrument that commits both sides to work to replace the backstop with alternative arrangements by December 2020.
"These are the legally binding changes that parliament asked us to secure".
If her deal is rejected again on Tuesday, the Labour leader said the PM should "shift her red lines and show not just that she is willing to meet with members of this House, but that she is willing to compromise with them too".
British lawmakers are scheduled to vote Tuesday on whether to approve May's Brexit deal, which they resoundingly rejected in January.
The MLA for Foyle commented: "Sooner or later, the British Parliament is going to have to support a Backstop for Northern Ireland or else support no Brexit at all; there is no happy medium between these two eventualities".
In preparation for today's vote, the government published details on how the government would proceed should Parliament decide to leave without an agreement.
She warned in a speech Friday that rejecting her deal again would create a "moment of crisis".
The vote deepened uncertainty for the future of Brexit, with no deal, a new deal and a delay all still on the table, The Metro reports.
Products from the European Union including beef, pork, chicken, butter, cheese and fish would also be subject to import taxes expected to push up prices in the supermarkets from March 29.
Parliament rejected May's deal by 230 votes on January 15, prompting her to return to Brussels in search of changes to address the so-called Irish backstop - an insurance policy created to prevent the return of a hard border between Ireland and Northern Ireland.
Cutting tariffs on imported goods would ease the hit to British consumers from an expected jump in inflation in the event of a no-deal Brexit which would probably cause sterling to tumble and make imports more expensive.
"This is a government in chaos, with a country in chaos because of this mess", Labour Party leader Jeremy Corbyn said.
"It does not reopen the withdrawal agreement, or undermine the backstop or its application".
Wilson said the DUP made a decision to vote against May's deal as soon as they read the legal advice by Britain's attorney general, which, he said, showed nothing had changed after Monday's revisions to the deal.
"The EU will want to know what use we mean to make of such an extension", she said.
May's deal again on March 12, lawmakers will vote over the following two days on whether to leave the European Union without an agreement - an idea likely to be rejected, or to ask the European Union to delay Brexit beyond the scheduled March 29 departure date.
May has staked her political reputation on securing an exit deal with the European Union, and is under mounting pressure to quit if it is defeated again.
The prime minister has since been trying to negotiate changes to the agreement, in particular regarding the highly unpopular backstop provision, which is created to ensure a frictionless Irish border and would, as many fear, tie the United Kingdom to the EU customs union.