"Our duty as a parliament over these coming weeks is to examine this deal in detail, to debate it respectfully, to listen to our constituents and decide what is in our national interest", May will tell lawmakers, according to advance excerpts from her statement.
However, Mrs May did receive some support when Japanese Prime Minister Shinzo Abe welcomed the fact she had reached a deal with Brussels in a telephone call between the two leaders.
European Commission President Jean-Claude Juncker said anyone hoping for fresh negotiations would be disappointed within "seconds" if Parliament rejects the deal, while Austrian Chancellor Sebastian Kurz added, "This is a take-it-or-leave-it situation.
No guarantee of smooth trade in the future and no ability to reduce the tariffs that we need to conclude trade deals with the rest of the world", Fallon told BBC radio.
"We have already been laying the groundwork for an ambitious agreement with the U.S. through our joint working groups, which have met five times so far".
European Council President Donald Tusk, after a special summit in Brussels this weekend, tweeted: "EU27 has endorsed the Withdrawal Agreement and Political Declaration on the future EU-UK relations".
"Sounds like a great deal for the European Union", said Trump speaking to reporters outside the White House on Monday.
"What my job is about is showing those MPs who will be voting on December 11 on this deal why it is a good deal for the United Kingdom".
"Having been told by the European Union that we would need to split the UK in two, we are leaving as one United Kingdom", May said in a statement announcing the visit and defending the border arrangements agreed with the EU.
Colum Eastwood, leader of Northern Ireland's moderate Irish nationalist Social Democratic and Labour Party (SDLP), on Monday urged lawmakers from Labour and other parties to back May's deal.More news: Liverpool boss Klopp shrugs off Henderson red after Watford rout
The vote in parliament is scheduled for December 11.
The Prime Minister's deal has received widespread opposition from MPs of all parties.
"Any debate must include an advocate of a clean Brexit who wants to fully deliver on the wishes of the British people".
Theresa May and the United Kingdom government refused to purse this despite most analysis suggesting it was the best option available.
"No one knows what would happen if this deal doesn't pass".
"The message I have clearly heard here today from across the board - from the voluntary sector, from young people, from businesses, from the cultural sector, from academics - is the importance of that certainty and the importance of Parliament accepting that deal so we can move on to develop our future", she said.
She claimed Mrs May was making a desperate, last ditch attempt to force her much-criticised deal through Parliament by attempting to "blackmail" MPs into voting for it.
"To Theresa May I would simply say 'what are you scared of, allowing people advocating these different options to take part in the debate?'"
May must now navigate the deal through a divided chamber in which she holds the slimmest working majority - and where lawmakers oppose it on all sides.
Downing Street has said the timing and nature of the debate has yet to be decided. The truth is, under this Government we have never got off square one.