May will hold a conference call with Cabinet ministers at 11:30 a.m. on her plans for the meaningful vote in Parliament, according to two people familiar with the matter.
"From listening to those views", she continued after the noise in the chamber ebbed, "it is clear that while there is broad support for numerous key aspects of the deal, on one issue - the Northern Ireland backstop - there remains widespread and deep concern".
Mrs Foster said: "My message was clear".
An updated House of Commons business statement said there would be a statement on "business of the House" after May's address, indicating a sudden change to the parliamentary schedule.
A standing-room only rally was held at the weekend, just days before a crucial vote in Parliament on the Government's proposed Brexit deal.
Last week May lost three votes in the Parliament on Brexit-related issues, a humiliation rarely visited upon a prime minister and one that did not bode well for the looming Brexit vote.
MPs could give Mrs May "a powerful mandate to change that backstop" by voting it down on Tuesday, he said.
The prime minister must submit a final deal for parliamentary approval by January 21, and the U.K.is set to leave the European Union - regardless of whether a deal is in hand - on March 29.
He dismissed suggestions he had already offered other Tory MPs jobs if they backed a future leadership bid by him as "nonsense" and said the public wanted to see a plan "to get out of this mess" rather than "stuff about leadership elections and personalities" - although he did not rule out challenging Mrs May for the leadership.
"As part of the government's Brexit deal, we'll lose all our rights as an European Union member with less trade, fewer opportunities, and lower living standards".
"This judgment exposes as false the idea that the only choice is between a bad deal negotiated by the United Kingdom government or the disaster of no deal".
"That's because it is a good deal, it's the only deal and it's important we don't let the flawless be the enemy of the good".
The prime minister is "not totally comfortable" with the backstop, Hunt said.
"It is impossible to deliver on the 2016 referendum result because it was based on false promises and fantasy".
They urged her to return to Brussels instead to try to secure more concessions before the House of Commons has the final say.
The EU Court of Justice in Luxembourg said Britain is free to revoke its so-called Article 50 notice any time before it's due to leave the bloc on March 29.
"Theresa May will come to the European summit on December 13 and 14 to ask for a renegotiation and the 27 will tell her no, the texts have been agreed", an informed European source told AFP on condition on anonymity.
But The Times said the main opposition Labour Party was seeking an alliance with rebel Conservatives and the Democratic Unionist Party, the small Northern Irish party which props up the minority government, to call a vote of no-confidence in May's premiership.