If they vote to leave with no deal, the United Kingdom will have left the European Union on March 29 and since there will be no deal in effect it is unclear what will happen in the immediate aftermath.
With EU leaders warning there would be no more changes or negotiations, and less than three weeks to go until the United Kingdom is due to leave, British lawmakers were facing a stark choice: support a deal many consider inadequate or run the risk that Brexit might happen chaotically, or not at all.
Speaking in the House of Commons as May announced the agreement, Cabinet Office minister and her de-facto deputy David Lidington said MPs would face a "fundamental choice" later today "to vote for the improved deal or to plunge this country into a political crisis". Geoffrey Cox, the government's top lawyer, is due to give his opinion on Tuesday at 1230 GMT ahead of the vote due around 1900 GMT.
The Attorney General said additions to the Brexit deal secured by the Prime Minister in last-minute talks with the European Union on Monday night "reduce the risk" of the insurance policy for the Irish border in the vent that Brussels acts with "bad faith or want of best endeavours" in negotiations on a future trade deal.
The pound, which had risen after May secured the changes in Strasbourg, went into reverse and tumbled after Mr Cox's advice was released.
The defeat came after May and European Commission President Jean-Claude Juncker announced changes Monday created to overcome lawmakers' concerns about provisions created to ensure the border between EU member Ireland and Britain's Northern Ireland remains open after Brexit.
They pressed Mrs May to secure the right for Britain to pull out of the arrangement or to make it time limited.
"The probability of some variant of this deal going through is falling rapidly and the probability of an alternative, nearly certainly softer, deal replacing it is rising", said Adam Cole, chief currency strategist at Royal Bank of Canada.
The House of Commons will vote later Tuesday after last-minute talks with the European Union produced assurances that May said means the deal couldn't be used to tie Britain to the bloc indefinitely.
British lawmakers, who on January 15 voted 432-202 against May's deal, were studying the assurances and Cox's legal advice before the vote later on Tuesday.
MPs will vote whether to leave without a deal.
Will Theresa May resign and will she be able to get her Brexit deal through Parliament?
"Today marks a momentous day in the Brexit journey to say the least".
May said the government would not instruct her own party's MPs how to vote, as would normally be the case.
"There will be no third chance", he said.
One eurosceptic lawmaker told Reuters he had seen nothing to change his opposition to the deal.
The U.K.is set to leave the bloc March 29 as a result of a 2016 referendum where British voters chose to leave the union after more than 40 years of membership.
That option is fraught with economic dangers and is backed only by hardcore proponents of the divorce.
Brexit-backing Tory backbencher Andrea Jenkyns tweeted: "Nothing has really changed, and it is still a bad deal so unable to vote for this". They have an opportunity to grand such a request at a March 21-22 summit in Brussels.
Any postponement may have to be short-lived.
German Chancellor Angela Merkel on Wednesday refused to say how long she thinks a possible delay to Brexit should be, but said it was in "our mutual interest that we achieve an orderly departure".