Brexit-supporting MPs have urged May to push for the Brexit deal to be renegotiated, while UK Labour leader Jeremy Corbyn has tabled an Urgent Question in the UK Parliament, asking Theresa May to make a statement on "progress made in achieving legal changes to the Withdrawal Agreement and the timetable in this House for the meaningful vote".
Her proposal is aimed at restricting the Government's freedom to use the Bill to make tax changes linked to a no-deal Brexit without the "explicit consent" of Parliament.
The government lost the vote by 296 votes to 303, with six former cabinet ministers - Ken Clarke, Michael Fallon, Justine Greening, Dominic Grieve, Oliver Letwin and Nicky Morgan - defying party orders and siding with Labour.
The prime minister has said the United Kingdom will be in "uncharted territory" if the deal is not accepted although she has not ruled out asking the Commons to vote on it on several times prior to the 29 March deadline.
The British leader said that since the vote was pulled at the last minute in December, she's been consulting with European Union leaders and British colleagues to get new assurances in three key areas, the details of which will be laid out in the coming days.
Earlier, Work and Pensions Secretary Amber Rudd told Cabinet colleagues history would take "a dim view" of them if they allowed Britain to leave the European Union without a deal.
With a raft of other legislation still needing to be approved before Brexit day, that signals further difficulties for the government if it pursues a no-deal exit.
She said: "No-deal is a awful deal and it would be a gross dereliction of the responsibility of members of this House to inflict a no-deal situation on our constituents".
The Prime Minister, who spoke to six European leaders including French President Emmanuel Macron and German Chancellor Angela Merkel over the Christmas holiday, said the government was "continuing to work on further assurances" on the issue of the controversial Irish border backstop.
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However, there are those who favour a No Deal Brexit and claim this would be inline with what people voted for in the referendum.
Some Brexit supporters say a no-deal exit is the only way to truly leave the bloc and that warnings of the economic consequences have been overblown to drum up support for May's plan. "I think it's those kind of assurances we are happy to give".
Speaking to Matt Stadlen, the Tory MP said that the Prime Minister's Brexit deal is the right option because the "British people are pragmatic".
"There was no suggestion that we would pay £39 billion for nothing, without even a sniff of a trade deal with Brussels".
Yet, the "concession", as Mr Lidington described it, has already been dismissed by the Democratic Unionists, who said: "We would be fools to accept any such assurance".
The vote had originally been scheduled for December 10, but May postponed it, admitting in the House of Commons that it would have been "rejected by a significant margin".
May has repeatedly said that the alternatives to her Brexit deal are "no deal" or "no Brexit".
"If the deal is not voted on at this vote that's coming up, then actually we're going to be in uncharted territory", May said on the BBC's Andrew Marr Show.
Parliament once again took back control of Brexit on Tuesday night as senior Tories rebelled against the government in a cross-party bid to block a "disastrous" no-deal.