European Union leaders approved the agreement on the UK's withdrawal from the bloc on Sunday after 20 months of negotiations. This raises the prospect of some of Mrs May's own MPs voting against the agreement when it goes before the Commons.
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.
But she admitted she was not "entirely happy" with the "backstop" contingency plan to avoid a hard border in Ireland.
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 Sunday, DUP leader Arlene Foster said there were no circumstances under which her party would vote for the current deal.
It comes amid growing signs the Brexit civil war rocking the Tories is sparking bitter in-fighting in Labour as the crunch vote looms in just a fortnight's time.
In his regular Daily Telegraph column, he said: "The other European Union countries have signed the deal immediately, because they know that they have us exactly where they want us". Labour said he would "relish" the opportunity.
So if you want to actually know the economic cost of the deal, Theresa May will attempt to sell to MPs on December 12 start with what the Treasury projects as the economic cost of Chequers compared with staying in the European Union and then knock off a bit more income.
She said rejecting it "would open the door to more division and more uncertainty, with all the risks that will entail".
EU Council President Donald Tusk, who has always said he would prefer Britain not to leave, said on the eve of the summit that "no-one will have reasons to be happy" when Brexit happens.
"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 4% lower than it would have been had the United Kingdom stayed in the EU", the NIESR said.
'For example to extend Article 50. According to reports, officials in Westminster and Brussels were continuing to work on plans for alternative arrangements.
In fairness to the Treasury, it was impossible for it to model the deal that was actually done at the weekend because in respect of the UK's future trading relationship with the EU, Theresa May's Brexit is myopic to the point of being semi-blind. Negotiators have until the end of the transition period, which could run until the end of 2022, to strike a deal. "They failed in the Withdrawal Agreement, and they failed again in the Political Declaration", May said.