Britain and the 27 other European Union leaders signed off on a Brexit deal Sunday after more than a year and a half of tough negotiations.
European Commission president Jean-Claude Juncker has warned Britain can not expect to get a better Brexit deal if Parliament rejects the agreement hammered out by Theresa May.
"Because no-one knows what would happen if this deal doesn't pass".
The two-hour meeting also heard an update from Mr Barclay on preparations for a possible no-deal Brexit, which are continuing despite the deal being agreed in Brussels. 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".
In a withering assessment of Mrs May's deal, Mr Trump said that it was "great" for the European Union but suggested it would harm the UK's ability to strike a trade deal with the US.
Conservative MP Mark Francois told May her deal was "as dead as a Dodo".
On Saturday, Chancellor Philip Hammond warned that rejecting the deal would leave Britain in "uncharted territory", while he said a no-deal Brexit would unleash "economic chaos".
The Labour leader said "ploughing on" with a deal opposed by the public and MPs was an "act of national self-harm".
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 told MPs the Government had ensured that Gibraltar was covered by the Withdrawal Agreement and would negotiate a future relationship "for the whole United Kingdom family, including Gibraltar".
But Labour leader Jeremy Corbyn said the Commons would have "very little choice" but to reject Mrs May's "botched" deal, which he described as "bad for this country". "They failed in the Withdrawal Agreement, and they failed again in the Political Declaration", May said.
She insisted "there is no deal that comes without a backstop and without a backstop there is no deal".
But Downing Street sources said they were not aware of the Prime Minister seeking to speak to Labour MPs thought to be considering backing her deal.
In her statement to MPs, Mrs May said there had been "give and take" in the 19-month negotiations but the final agreement "delivered for the British people" by regaining control of laws, money and borders.
With scores of MPs declaring their intention to vote the deal down, the Brexit Secretary was asked on BBC Radio 4's Today programme how the Government will get it through Parliament.