Hard-line Brexit supporters in May's Conservative Party said she should postpone Tuesday's vote rather than risk another crushing defeat.
On the border, the UK Government said it would remove all checks except a "small number of measures strictly to comply with global obligations, protect the biosecurity of the island of Ireland, or to avoid the highest risks to Northern Ireland business".
At a late-night news conference Monday in Strasbourg, France, May and European Commission President Jean-Claude Juncker announced changes 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.
It comes after the Brexit Withdrawal Agreement was rejected by 149 votes in the House of Commons last night.
May has promised Britain will leave the European Union whatever happens on March 29, but many MPs fear that a "no deal" exit would wreak economic havoc.
Late Monday, Cabinet Office Minister David Lidington announced in the House of Commons that the two sides had agreed on "legally binding changes" to a portion of the deal relating to the Irish border. The plans cover how to avoid a hard border with Ireland and what tariffs would take effect.
Yet May has not given up on a third attempt to get her deal through Parliament again.
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.
He said that "we are waiting now for a proposal coming from London".
He said he is "deeply disappointed" with the outcome of the meaningful vote in Westminster tonight.
That, in turn, would make such options as a new Brexit referendum or a "softer" withdrawal from the European Union lot more likely, he said.
"These will cover our approach to tariffs and the Northern Ireland border among other matters".
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"It hasn't been possible to do that this evening".
They urged her to table a "conditional" motion setting out the terms for dealing with the backstop issue which Parliament would be prepared to accept.
The Daily Mail says there is now speculation over how long Mrs May will remain as Prime Minister, although her aides have insisted she has not considered resigning.
The European Parliament, meanwhile, approved measures to ameliorate the immediate hardships of a no-deal Brexit.
European Commission chief Jean-Claude Juncker warned that the stakes were increasingly high, ahead of a vote by British lawmakers on the deal on Tuesday.
However, lawmakers are expected to vote against a no-deal Brexit and then, on Thursday, vote in favour of seeking a delay to Brexit.
However, Britain's attorney general, Geoffrey Cox said the assurances Mrs May had been given still meant the United Kingdom could be locked in the bloc's orbit after Brexit. "However, the matter of law affecting withdrawal can only inform what is essentially a political decision that each of us must make".
"Let me be clear: the only legal basis for a transition is the WA".
"The Withdrawal Agreement is imperfect but it is the only deal on offer".
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".
"We need radical change. and we need to see some steel in her stance", he said. MPs have also been promised they will be shown any updated legal advice from Attorney General Geoffrey Cox before the debate begins.