It was negotiated over 18 months with the United Kingdom and by the UK.
May backed a proposal from a Conservative backbencher calling for the backstop to be replaced by "alternative arrangements", and called on all lawmakers from her Conservative Party to support it.
It would force May to delay Brexit for nine months if her deal is not approved before February 26, and give lawmakers the ability to indefinitely extend the deadline.
A reporter for The Times said officials on "both sides of Brexit talks" had described it as "no plan at all" and "bonkers".
Conservative MPs were informed on Monday evening that they would be whipped to vote for the amendment - assuming it is selected by Commons Speaker John Bercow.
It calls for the backstop to be renegotiated or if that fails to leave on World Trade Organization rules at the end of 2021.
She added that May's secrecy and reliance on a small group of people had been a "handicap" in getting support for the deal.
Former foreign secretary Boris Johnson said winning a "freedom clause" would be "unadulterated good Brexit news".
Mrs May was coming under pressure from Conservative colleagues and the Democratic Unionist Party to seek further concessions from Brussels on the so-called "backstop" arrangements created to keep the Irish border open after Brexit.
It comes as Theresa May addressed a meeting of Tory MPs, the day before all MPs vote on a series of amendments to the PM's plans that could shape the future direction of Brexit.
But what will come first is the vote in the Commons, and Mrs May appealed for the backing of the "Brady" amendment as the next step, saying it would "give the mandate I need to negotiate with Brussels an arrangement that commands a majority in this House - not a further exchange of letters, but a significant and legally binding change to the withdrawal agreement".
Fourteen Labour MPs opted to reject the so-called Cooper amendment, which was said to have been supported by Jeremy Corbyn's shadow cabinet.
"Most of the amendments before us do not provide that".
Most members of Parliament oppose leaving without a deal, but they rejected several proposals that tried to wrest control of the Brexit process from the government and give it to Parliament so lawmakers could stop Britain crashing out of the European Union without a deal.
She was expected to tell MPs that the government hoped to bring back a deal to Parliament to secure the support of MPs in another "meaningful vote", as soon as possible.
European Union leaders have repeatedly urged Britain to clarify what kind of Brexit it wants and are watching to see which proposals - if any - get the backing of Parliament.
Ms Weyand said the ratification of the EU-UK deal would build the trust necessary to build a new relationship, but ruled out bowing to British calls to set a time limit to the backstop beyond which the insurance policy would lapse.
May, who will close Tuesday's debate, now hopes her Tory party will say clearly what it wants to change in the deal she's struck with the EU.
"There appears to be no majority in the House of Commons in favour of a no deal exit, although that remains the default outcome if the House of Commons is unable to approve the deal that has been reached or pass the legislation required to implement it in domestic law", the committee said.
"One that ensures we leave with a deal and and addresses the House's concerns while guaranteeing no return to the hard border between Ireland and Northern Ireland". "The [UK] negotiators have not been able to explain them to us and that's not their fault, it's because they don't exist".