May is due to meet Dutch Prime Minister Mark Rutte and German Chancellor Angela Merkel on Tuesday, Downing Street said.
"If we went ahead and held the vote tomorrow the deal would be rejected by a significant margin", May told parliament.
Briefing EU lawmakers in Strasbourg, France, on this week's leader's summit, Juncker said Tuesday that "there is no room whatsoever for renegotiation" of the divorce deal.
During the meeting, Juncker went on to say that the European Union was willing provide greater clarity over the Irish backstop plan to stop a hard border between Northern Ireland and the Irish Republic forming post-Brexit.
With time running out until March 29 when the United Kingdom is due to leave the EU, European leaders however have warned that the EU deal is not up for renegotiation, though the European Court of Justice confirmed Britain could unilaterally cancel Article 50.
Mrs May said she would do all she could to secure further assurances from the European Union on the so-called Northern Ireland backstop arrangement, a crucial part of the deal bitterly opposed by many of her fellow conservatives and opposition parties.
Chief among MPs" concerns is the status of the Northern Ireland "backstop', which is created to ensure that there is no return to a hard border on the island of Ireland.
"I think it is a good deal, it is the best deal and to approve this deal would be a good thing".
The speaker of the lower house of parliament, John Bercow, called for lawmakers to be given a vote on the decision to defer the vote on the deal itself.
"The prime minister set out the concerns held by many about it in the UK".
Any such undertakings would be "completely irrelevant" if they were not included in the withdrawal agreement, MP Jacob Rees-Mogg, a leading Brexit supporter, told reporters.
And a spokeswoman for European Commission president Jean-Claude Juncker poured cold water on any prospect of a renegotiation of the Withdrawal Agreement.
He said: 'The government is in disarray, uncertainty is building, uncertainty is building for business, people are in despair at the state of these failed negotiations and concerned about what it means for their jobs and communities - and the fault of that lies exclusively at the door of this shambolic government'. She will consider ways of how MPs can be given a say over the introduction of a backstop.
"It is necessary for the entire coherence of what we have agreed with Britain, and it is necessary for Ireland", Juncker said.
"I imagine they'll add some language saying that both sides remain convinced that we'll never need to use the backstop".
May said she still meant to put her deal to lawmakers.
The Labour Party was urged by other smaller opposition parties to trigger a vote of no confidence in the Government but said it would not act right away.
Anand Menon, European politics professor at King's College London, said May needed Brussels to make it "absolutely clear" no major concessions are on offer - no matter who is prime minister.
"I still believe there is a majority to be won in this House in support of it if I can secure additional reassurance on the question of the backstop", she told MPs.
"The government has lost control of events and is in complete disarray", said opposition leader Jeremy Corbyn.
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