She was loudly barracked by MPs as she insisted that no better deal was available than the Withdrawal Agreement and Political Declaration on future relations endorsed by European Union leaders in Brussels on Sunday.
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.
Former Tory leader Iain Duncan Smith questioned why the backstop was in the withdrawal agreement at all, saying it would result in "intolerable pressure" being applied on the United Kingdom to avoid it.
Britain was scheduled to leave the economic and political union on March 29, 2019.
He suggested Parliament would have "little choice" to reject the deal when MPs vote on it - expected to be in just over a fortnight's time.
She said: "I'm looking ahead to December 11th, when this House will be faced with a decision as to whether or not it wishes to deliver on the vote of the British people with a deal that not only delivers on that vote but also protects their jobs".
"Prime Minister I plead with you, the House of Commons has never ever surrendered to anybody and it won't start now".
European Commission president Jean-Claude Juncker warned that there would be no more negotiation if MPs vote down the agreement, telling the BBC: "This is the best deal for Britain. and this is the only deal possible, so if the House says no, we would have no deal".
Legislators on both sides hate the deal, a compromise that keeps Britain outside the European Union with no say but still subject to the rules and the obligations of membership at least until the end of 2020 while a permanent new relationship is worked out.
The Prime Minister can't count on the 10 DUP MPs with whom she has a confidence and supply deal.
Dozens of Conservative legislators say they will reject the deal, either because they want a harder or a softer break with the EU.
She said rejecting it "would open the door to more division and more uncertainty, with all the risks that will entail".
In other words, we will be asked by the Treasury to compare two scenarios that the PM herself admits could yet happen - particularly no Brexit and a non-deal Brexit - with one scenario, Chequers, that cannot possibly happen. 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".
"They failed in the Withdrawal Agreement, and they failed again in the Political Declaration".