DUP leader Arlene Foster - whose 10 MPs prop up the minority Conservative administration in the Commons - said it provided a "feasible" alternative to the backstop. If it is defeated, she will table another amendable motion for debate the following day.
"This Withdrawal Agreement has been agreed with the United Kingdom government, is endorsed by leaders, and is not open for renegotiation", the European Commission spokesman told the journalists.
German Chancellor Angela Merkel said: "Both documents need to be ready by Sunday so that we can sign the exit agreement and accept the declaration on the future relationship".
She said it was a challenge to see how a majority for any deal could be built among MPs.
The retailers explain how the complex, "just in time" supply chain will be significantly disrupted in the event of no deal, even if the UK Government does not undertake checks on products at the border, there will still be major disruption at Calais as the French government has said it will enforce sanitary and customs checks on exports from the EU. It is hard to say owing to the many moving parts in parliament and a constant Brexit newsflow, but we would expect it to fall back into the ranges witnessed in December which would be more consistent with a higher chance of "no deal" Brexit being priced back into the market's thinking.
"People like me want to avoid a no-deal outcome, a crashing out on March 29".
If not, parliament would be given a vote on asking the European Union for a postponement of the Article 50 deadline to prevent Britain leaving without a deal on March 29.
But, two weeks ago, May told Parliament the "simple truth" was that the European Union was "not prepared to agree" to a unilateral exit mechanism from the backstop, or a time limit.
May has said she wants to secure concessions relating to the border with Northern Ireland in order to win the support of pro-Brexit lawmakers in her own party and the small Northern Irish party which props up her government, who voted against her deal.
But Green Party legislator Caroline Lucas accused May of chasing "heated-up fantasies that have already been rejected by the European Union". The PM was also willing to give the parliament another opportunity to vote for the Brexit deal as soon as possible.
Dover MP Charlie Elphicke said he had been won round by the Prime Minister after he urged her during the debate not to allow an extension to Article 50 and to ensure the government "honoured the referendum result" and ensure Labour's wrecking tactics did not succeed.
Speaking on BBC Graham said, "I'm hoping that the way in which the amendment is crafted, it can attract that very broad support. We have the vote tonight and then we will take it from there", he said.
Labour's amendment instructs the government to rule out a "no deal scenario" and allows Parliament to consider - and vote on - options including an alternative Brexit deal and legislating to hold a public vote.
The Institute for Government's Jill Rutter described it as "unnegotiable", based on ideas that had been rejected "time and again" by Brussels.
Mrs May backed a proposal from a Conservative politician calling for the Irish backstop to be replaced.
However, the joint political declaration on future relations - still being drafted - would only set out the shape of the UK's trading relationship with the remaining 27-nation bloc, without any legal commitments.
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 the U.K. Parliament. "That will mean reopening the withdrawal agreement".
The understands the intention is still to present a completed text to leaders at Sunday's summit but opinions differ over how easy it would be to solve the outstanding issues.
Former Conservative minister Caroline Spelman and Labour's Jack Dromey have joined forces to table an amendment to stop a no-deal Brexit.