That's because May has been unable to persuade Brussels to change the agreement, which her team negotiated past year, and put in legally binding reassurances that the United Kingdom will not become trapped in a long-term customs arrangement with the European Union.
In the past few hours Mrs May held a late-night meeting with the European Commission President Jean-Claude Juncker in Strasbourg to secure the agreement.
The UK has been seeking changes to the Irish backstop, an insurance policy created to maintain an open border on the island of Ireland between UK territory Northern Ireland and European Union member-state - the Republic of Ireland.
She has also been trying to win over Labour MPs from leave-voting constituencies with a 1.6 billion pounds ($2.1bn) fund and promises of more workers' rights.
Meanwhile, the prime minister's office refuted as "complete speculation" the media reports that the United Kingdom government could switch a meaningful Brexit vote in the Commons on Tuesday to an indicative one.
On Monday, May was closeted in talks with close aides in Downing Street, while a spokesperson insisted she had no plans to make a last-minute dash to Brussels and dismissed claims that the vote would be withdrawn due to the likelihood of it being voted down again.
He said: "If all that's happening is to turn this letter into an interpretative tool for legal purposes, I remind the House what the Prime Minister said on January 14 about this letter".
But if the lawmakers reject to leave the European Union without a deal, another vote will be held on Thursday, March 14.
Britain's Parliament is due to vote Tuesday on the withdrawal agreement, which it has already rejected once.
After that expected defeat, the Commons will vote on Wednesday over whether to keep a no deal Brexit on the table. Then there will be a vote on postponing the March 29 exit day.
May's spokesman, James Slack, said "talks are ongoing" among lower-level negotiators and there was "a shared determination by both sides to find a solution".
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"We remain optimistic that a hard Brexit will be avoided, and that in our view should put a floor on GBP", said Rodrigo Catril, a senior foreign-exchange strategist at National Australia Bank Ltd.in Sydney.
The EU has rejected many of May's demands, which relate to the controversial backstop plan for the Irish border, but German Chancellor Angela Merkel said it had made an offer at the weekend.
"The choice is clear: it is this deal, or Brexit may not happen at all".
Sterling see-sawed on Brexit news, falling in early trade on speculation that May could cancel the vote in parliament but later rising on news that May could travel to Strasbourg.
May is hoping for a different outcome to the historic defeat her last divorce deal suffered in January. "Benjamin Franklin said of the U.S. Constitution, "I vote for this with all its faults" and I think that's the approach that we need to take on Tuesday", Hancock told Sky News.
Eurosceptics might be persuaded to vote for May's deal if they believe that Brexit may be cancelled altogether.
May has already survived a leadership challenge from within the Conservative Party, which means there can not be another one before December.
Labour has come out in favor of a second vote - albeit with some reservations.
The airline is to put plans in place to protect themselves from a no-deal and wants to ensure they will remain a majority European Union controlled and owned airline.
There has been speculation that the beleaguered prime minister may be forced to resign.