Mrs May will strike an upbeat tone when she gives a speech to business chiefs at the CBI conference today.
May then faced a hostile three-hour session in the House of Commons, during which there was open revolt from her own party and the DUP as well as all opposition parties.
She suggested agreeing more details of UK's future relationship with the European Union, ahead of an expected summit next week, could satisfy the concerns of some of the Tory MPs opposed to her plans.
As an aftermath, over 20 lawmakers submitted their letters of no-confidence and 48 letters are required for a leadership challenge vote.
"I would expect so", said the ERG's Crispin Blunt, asked whether the target would be hit.
"A sensible deal must guarantee a strong single market relationship", Corbyn said.
Speaking on Sophy Ridge on Sunday on Sky News, May said internal critics thinking of replacing her as Conservative leader should think again.
And in a warning to those pushing for a change of leader, she said: "It is not going to make the negotiations any easier and it won't change the parliamentary arithmetic".
Oxford West and Abingdon MP Layla Moran said she felt the deal "threatened" businesses, the NHS, schools and universities in Oxford. "Of course it has been a tough week, actually these negotiations have been tough right from the start, but they were always going to get even more hard right toward the end when we are coming to that conclusion".
"It offers that essential transitional period as a step back from the cliff-edge", she said.
Sir Graham told BBC Radio 5 Live that not even his wife knows how many letters he has received from other Conservative MPs. Like a shark circling under the water, the number of letters could be growing, could reach 48 and surface to bite her at any time.
The deal itself provoked strong opinions with only 4 per cent saying they neither support nor oppose the deal.
Forty-eight are needed to trigger a vote of no confidence.
"My deal or no deal": May defends Brexit divorce plan amid MP rebellion & cabinet resignations Amid a string of resignations and huge backlash from rebel MPs, Prime Minister Theresa May still believes her draft Brexit deal with the European Union will help secure British jobs, protect borders, and smooth the UK's exit from the bloc.
In response to resignations she has appointed former home secretary Amber Rudd, who quit over the Windrush scandal, back into the Cabinet to replace McVey at the DWP. The final stage was always going to be the toughest.
Describing the campaign by her fellow Brexiteers to oust the PM as a "burning fuse" despite them failing to muster enough numbers to bring around a vote of no confidence.
After spending a week having discussions and meetings with politicians and their advisers in Westminster, trying to work out where the story would fall by Sunday and secure the best people to talk about it, I finally got the calls confirming the guests.
He said: "We now need to keep up the momentum to finalise the withdrawal agreement and outline political declaration and deliver a Brexit that works for the whole United Kingdom".
Labour leader Jeremy Corbyn will also speak at the conference.