The European leaders on Sunday endorsed the Brexit deal at the EU summit in a major breakthrough since the lengthy Britain-EU Brexit negotiation started one and half years ago.
Mr Smith sought to spread some Christmas cheer to Conservatives feeling frosty towards Mrs May's deal in the letter, wishing MPs and their families "a very happy Christmas" and thanking them for their support this year.
Mrs May made the announcement in her third statement to the Commons on leaving the EU.
His warning came as European Union leaders gathered in Brussels endorsed the terms of the Withdrawal Agreement and the Political Declaration finally agreed with the commission last week.
"Our key finding is that if the Government's proposed Brexit deal is implemented so that the United Kingdom leaves the EU Customs Union and Single Market in 2021, then by 2030 GDP will be around four per cent lower than it would have been had the United Kingdom stayed in the EU", the report said.
Brexit enters into force on March 29 and May´s government is also making "no-deal" preparations just in case.
No 10 said it was well aware of the scale of the opposition.
"I do think she has everything now to argue for a yes vote in the British Parliament".
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"Given there are some 80 Conservative backbenchers who will vote against any deal come what may, in the national interest will the Prime Minister sit down with the leader of the Opposition and have a meaningful discussion about how we can make sure that, when it comes to workers' rights, health and safety, we don't fall behind and we secure a sustainable customs arrangement?"
The independent analysis has been commissioned by the People's Vote campaign, which is calling for another public vote on Mrs May's final Brexit deal.
Mrs May said the deal would deliver on jobs, but queried Mr Corbyn's commitment to a deal. On Sunday, DUP leader Arlene Foster said there were no circumstances under which her party would vote for the current deal.
"I can say to the House with absolute certainty that there is not a better deal available", May said.
"No one knows what would happen if this deal didn't pass", May told the House of Commons. On Monday, Mrs May is expected to tell the Commons that rejecting the deal would "open the door to more division and more uncertainty, with all the risks that will entail". Jeremy Corbyn has said the deal does not meet the tests and "is the result of a miserable failure of negotiation that leaves us with the worst of all worlds".
"We don´t want to give the wrong impression to people, whether they are passionate Remainers or passionate Brexiteers, that there is another agreement that can command the support of 28 member states".
"They failed in the Withdrawal Agreement, and they failed again in the Political Declaration".