Mrs May later spoke by phone to Arlene Foster, leader of the Democratic Unionist Party, whose MPs prop up the minority Conservative administration but were threatening to vote against her deal.
"The clear message is that Prime Minister Theresa May must give the public a final say on the Brexit deal, with the option to stay in the European Union".
An updated House of Commons schedule said there would also be a statement on "business of the House" after May's address, indicating a sudden change to the parliamentary timetable.
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.
SNP deputy Westminster leader Kirsty Blackman has accused the UK Government of being in a "total state of chaos" over the prime minister's Brexit deal.
"Everyone knows what the bone of contention is - the backstop - and there are a large number of MPs who are prepared to compromise", Brady said.
On March 29, 2017, Prime Minister Theresa May formally notified the European Union of the U.K.'s intention to leave, starting the two-year negotiating period spelled out in the bloc's rules. May said the prospects of opposition leader "Jeremy Corbyn getting his hands on power is a risk we can not afford to take".
"If you want Brexit, make sure you get it, and that's about this deal", she said.
The DUP is unhappy that the deal will see Northern Ireland aligned with European Union rules and remain part of the single market with checks on some goods coming in from the United Kingdom to Northern Ireland, if the Brexit backstop is implemented.
The Prime Minister is due to travel to Brussels on Thursday for an EU Summit, and said she would be speaking with EU leaders ahead of her trip. Now the prime minister can go to Brussels and renegotiate, he added.
May insisted that her Brexit deal was still "the best deal that is negotiable", and said rejecting it raised the chances of Britain crashing out of the European Union with no agreement, bringing logjams to British ports and plunging the country possibly into the deepest recession in decades.
'Anxiety may have being triggered by Brexit - but the future and functioning of the government is now also a threat for the pound'.
She said the broader question was whether parliament wanted to deliver on the will of the people for Brexit, or open up the divisions in the world's fifth largest economy with another referendum.
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. Demonstrators expressed concern about what they say is the growth of the far right in the country.
One cabinet minister told The Observer that the PM was so committed to the deal that "a second referendum could now be the only way of getting it".
Under the Fixed Term Parliament Act, the opposition would have to win a vote of no confidence in the PM in the Commons and then hope the Conservatives could put together a Government which could win a second vote, in which case a general election would be called.