"Not after a no-deal, this is when it has became apparent that a no-deal is the only likely option", McEntee told national broadcaster RTE.
On the border, the UK Government said it would remove all checks except a "small number of measures strictly to comply with worldwide obligations, protect the biosecurity of the island of Ireland, or to avoid the highest risks to Northern Ireland business".
The Daily Mirror says Mrs May's defeat was "humiliating" and her authority has been left "in tatters".
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.
Lawmakers defeated May's deal by a whopping 230 votes in January, but May hoped the changes she secured from the bloc would be enough to persuade many to change their minds.
Political leaders around Europe reacted with disappointment to last night's vote.
The main opposition Labour party still opposes the deal, even while May has been wooing individual MPs with promises of protection for workers' rights and new funds for poor towns.
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Tonight MPs will vote again tomorrow on no deal and then on delaying Brexit on Thursday - votes set to unlock a cascade of consequences including a softer Brexit, a second referendum and not leaving the European Union at all.
Yesterday, Mrs May rushed to Strasbourg to agree legally binding assurances with European Commission President Jean-Claude Juncker.
Michael Gove, who campaigned for Brexit in 2016, said that if May lost Tuesday's vote then it would effectively lose control of Brexit.
Labour plans to make its MPs vote for an amendment at a later date, which would put Theresa May's deal to the country in a second referendum in an effort to break through Parliamentary deadlock.
The Telegraph said there was "a backdrop of exasperation" to the Prime Minister's trip to Brussels and that a deal will only succeed if there is "no doubt" that the backstop is temporary. Business leaders, who are already appalled at the failure of the British government to resolve Brexit, would be furious if the country crashed out of the European Union after two years of negotiations.
Parliament was due to vote later Wednesday on whether to rule out leaving the European Union on March 29 without a deal - though that won't eliminate the risk it could happen anyway.
"If we leave without a deal, we will set the majority of our import tariffs to zero, whilst maintaining tariffs for the most sensitive industries", Trade Policy Minister George Hollingbery said.
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Mr Lidington told MPs in a late night sitting in the Commons that the PM had secured legally binding changes that "strengthened and improved" the withdrawal agreement.
If lawmakers reject a no-deal exit, the government will hold a vote on Thursday to ask parliament whether Brexit should be delayed.
Many business leaders have spoken about the potentially disastrous consequences of a no-deal Brexit.
Many products that now trade seamlessly between the United Kingdom and the EU would be expected to face tariffs and inspections when Britain leaves the European Union near the end of this month.
"Finally, the House of Commons is going to have to make a final judgement on what it wants in terms of Brexit", he said.
Some British lawmakers warned their Brexit-backing colleagues that rejecting the deal could lead to Britain's departure being postponed indefinitely, because a delay would give momentum to opponents of Brexit.
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