"It's about people's jobs and about their livelihoods, and I think they would expect us to do this seriously".
May has warned sceptical members of parliament that if they reject the deal the world's fifth largest economy will either leave without an agreement or Brexit could be delayed or even reversed.
He added: "We want to exercise our ancient parliamentary privileges to tell our MPs that we don't think this deal is good enough and we desperately want you to reject the deal and give us a People's Vote".
In her address to MPs on Monday, Theresa May will warn them that if they vote it down Britain could face leaving the European Union without a deal - something businesses say could reflect very negatively on the country's economy, and lead to "more division and more uncertainty".
If the Prime Minister's deal is going to get through the Commons, she may be forced to rely on the votes of Labour MPs from Leave-supporting areas.
She added: "Nothing has been settled in terms of when the debate will take place but I think this is an important moment for our country and it is right that we treat it with the seriousness it deserves".
"I am willing to stand up and explain why I think it is the best possible deal available for the United Kingdom", she told The Sun. May has said that a general election is not in the national interest.
The Prime Minister has embarked on a national campaign to convince voters and politicians that her deal is the best and only one available for delivering Brexit.
'This is a bad deal for the country. "It would open the door to more division and more uncertainty, with all the risks that will entail".
"I think we have got to do all that we can and I am hoping that it will have an impact and that MPs will spare five minutes of their day to come down and talk to the generation that is going to have to bear the consequences of this decision for the longest". They outline how important issues such as citizens' rights, the Irish border, and trade will be handled when the United Kingdom leaves the European Union on 29 March 2019. May has said she will not call a second referendum.
Mrs May was also asked whether she was losing support for her Brexit deal after former defence secretary Sir Michael Fallon said he would not be supporting it in Parliament.
The head of the Northern Irish party which props up her minority government but opposes May's Brexit agreement said the prime minister was "wasting time" touring instead of fighting for a new deal.
"I believe we have a good deal for the United Kingdom, it delivers on the Brexit vote, it protects people's jobs".
- L.A. Auto Show: Honda Passport returns for 2019
- 'To All The Boys I've Loved Before' Sequel Confirmed
- Turkish police search villas as part of Khashoggi case probe
- Kate Middleton Reveals Feelings on Meghan Markle's Pregnancy Amid Rumoured Spat
- Trump ex-lawyer Cohen pleads guilty to lying to Congress
- Deutsche Bank offices raided in Panama Papers money laundering probe
- Mississippi Senate runoff nears finale
- Stephen Curry responds to message from fan over no women’s shoe
- Nintendo Creators Program axed, YouTubers and Twitchers rejoice
- Scientist who claims he edited twins' genes apologises … for result being leaked