She is expected to have phone calls with key EU leaders throughout the day ahead of a series of Commons votes over the future direction of Brexit, and has already spoken to the President of the European Commission Jean-Claude Juncker and the Irish Taoiseach (Prime Minister) Leo Varadkar.
She had issued a plea for MPs to give her a clear "mandate" to reopen the Withdrawal Agreement which she agreed with the European Union last November and seek to secure changes to its controversial backstop provision.
Speaking to BBC Radio 4's Today programme, Duncan Smith said today that the proposal was "the best hope we've got".
Mrs May admitted Parliament had made clear what they did not want when they rejected her Withdrawal Agreement by a 230-vote margin earlier this month, but now it was time for them to tell Brussels what they do want.
She said it was a chance to "tell Brussels that the current nature of the backstop is the key reason Parliament can not support this deal".
It's far from certain the amendment will win support from a majority in the House of Commons when it comes to a vote later Wednesday.
The Brexit deal between London and Brussels - overwhelmingly rejected this month by British MPs - contains a so-called backstop provision ensuring that if all else fails, the border will remain open.
He was questioned about how this strategy might work, given how often the European Union has said it will not reopen the Brexit agreement.
Mr Macron called on Mrs May to present the EU's chief negotiator Michel Barnier with her next steps for avoiding a no-deal Brexit on March 29, which he said "no-one wants, but ... we must all, despite everything, prepare for".
"If you want Brexit, you have to vote for Brexit".
Cooper's amendment seeks to shift control of Brexit from May's government to Parliament, and if successful could have a profound effect, giving lawmakers who want to block, delay or renegotiate Brexit a possible legal route to do so.
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As the crisis over European Union membership approaches its finale, the possible outcomes include a no-deal Brexit, a last-minute deal, a delay, a snap election, or even a referendum that could undo the 2016 Brexit vote.
Last amendment of the night, and one supported by the government.
Ireland's European Affairs Minister, Helen McEntee, said British politicians needed to show "a bit of realism".
Following the vote, Labour leader Jeremy Corbyn said he would be willing to enter into Brexit talks with Mrs May.
If they say no, again, the day before Valentine's Day May will come back to tell Parliament their lust for a new Brexit divorce deal must remain unrequited.
The Prime Minister's Brexit deal proved so unpopular the government fell to a historic defeat when parliament voted on it in December, losing by a record 232 votes.
Other Labour MPs who voted with the government to vote down the Cooper amendment included Ian Austin, Sir Kevin Barron, Ronnie Campbell, Rosie Cooper, Jim Fitzpatrick, Roger Godsiff, Stephen Hepburn, John Mann and Gareth Snell.
She also refused to rule out the prospect of resigning in order to vote against the Cooper amendment.
But he insisted: "What we need is to achieve something legally binding - and that means part of the Withdrawal Agreement".
The Unionist Party believes it is feasible.
In a note of criticism of May's strategy, she said there appeared to be a lack of "ownership" in Britain of the agreement struck between the two sides in November, and that there was insufficient transparency in the prime minister's moves. "(They) have the vote tonight and then we will take it from there".