Announcing the delay, May was laughed at by some MPs when she said there was broad support for the deal and that she had listened carefully to different views over it - the result of 18 months of tortuous negotiations.
An analysis by Britain's Press Association showed that just 27 of the 163 British lawmakers who have spoken out indicated they would back May's deal, compared with 122 - including 29 from May's own Conservative Party - who say they will vote against it.
That window for the U.K.is open so long as it hasn't implemented a final Brexit agreement with the European Union - and would remain open until Article 50 was due to take effect in March.
He said that although the government could defer it unilaterally, he would be happy to facilitate a vote on the matter. "This shambles can't go on - so how about it?"
May's comments came after she postponed a vote scheduled for Tuesday on the European Union divorce deal, acknowledging she would have lost by a "significant margin".
The leaders of Northern Ireland's four Remain parties (Sinn Fein, SDLP, Green Party and Alliance Party) have issued a statement saying that the backstop must be retained.
The document, which May calls "the best possible deal", is criticized by both Conservatives and the opposition.
"It matters certainly to them, but it matters a great deal to us as well", he said.
Liberal Democrat Leader Sir Vince Cable said the government had "lost all authority", adding that he would support a confidence motion if Labour tables one.More news: Google Pixel 3 Lite & Pixel 3 Lite XL CAD Renders Revealed!
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FILE- In this December 8, 2017 file photo, UK's Union Flag, left, and the EU flag, flap in the wind outside EU headquarters in Brussels.
Pro-Brexit lawmakers say May's deal keeps Britain bound too closely to the European Union, while pro-EU politicians say it erects barriers between the United Kingdom and its biggest trading partner and leaves many details of the future relationship undecided. An undeliverable deal parliament would roundly reject, if the Prime Minister has the gumption to allow it to go before the House of Commons. Pro-EU lawmakers want a softer divorce - the so-called Norway option - that would keep Britain inside the EU's single market for goods and services. It was trading at $1.50 on the day of the 2016 Brexit referendum.
Brexit Secretary Stephen Barclay will then make a statement to MPs on the Article 50 process.
The former minister, now a senior member of the Brexiteer European Research Group (ERG), added: "This is essentially a defeat of the Prime Minister's Brexit deal".
The case was brought to the European Court of Justice by a cross-party group of Scottish lawmakers.
The Luxembourg-based ECJ said that given the absence of any exit provision in Article 50, countries are able to change their mind in line with their own constitutional arrangements and that such a move "reflects a sovereign decision".
May has repeatedly said the government will not seek to delay or reverse Brexit.
Mr Johnson, who quit the cabinet over Mrs May's Brexit strategy, told the BBC he did not want a "no-deal" Brexit or another referendum, but it was not right to say there were no alternatives.