As furious Conservative rebels try to gather the numbers to trigger a no-confidence vote, May insisted she hadn't considered quitting.
By Sunday afternoon, a total of 25 MPs had revealed they had sent no-confidence letters to the chairman of the party's 1922 Committee, Sir Graham Brady.
Mrs May said she would travel to Brussels this week to meet European Commission President Jean-Claude Juncker.
Mr McFadden said: "If she can not get the agreement through Parliament then I think we have to put the issue back to the people".
Leadsom leads a group of Brexiteer Cabinet ministers who want to tweak the deal - but that possibility was last night shot down by Simon Coveney, in a podcast from the Fine Gael Ard Fheis.
Mordaunt, Raab, and five other top Conservatives - former Foreign Secretary Boris Johnson, Raab's predecessor David Davis, Interior Minister Sajid Javid, Foreign Secretary Jeremy Hunt, and Work and Pensions Minister Amber Rudd - are all "actively preparing" leadership campaigns, the Sunday Times said.
May defended her deal on Sky news on Sunday, describing it 'as the right deal in the national interest.' She faces intense pressure from an alliance of hardline Brexit supporters within her party who want her to re-enter negotiations with the EU.
Labour leader Mr Corbyn says his party, which has 257 MPs, will not support the deal. "Politics is a tough business and I've been in it for a long time".
The future relationship between the Republic of Ireland and the british province of Northern Ireland is indeed one of the issues still sensitive to the agreement on the Brexit.
Last year, Mrs May was forced to promise a meaningful vote on any Brexit deal after 11 pro-EU voted with opposition parties.
Raab said the message had not reached European Union negotiators that Britain would not be "blackmailed and bullied" by Brussels.
"I am confident that we can strike a deal at the Council that I can take back to the House of Commons". She would remain prime minister until the contest was over unless she opted to resign and hand over to a caretaker prime minister.
If no other solution can be found, the backstop will apply following a 21-month transitional period to keep an open border between the Republic of Ireland, which will remain an European Union member, and Northern Ireland, which will leave the bloc with the rest of the United Kingdom.
In Dublin, the irish Prime minister, Leo Varadkar, has recalled the position of his country.
Gosport MP Caroline Dinenage says that although she hasn't seen the full deal yet, she will also be backing Theresa May in the coming months.
But both sides are scrambling to finalise a parallel political declaration that will set out a road-map for post-Brexit negotiations on future EU-UK ties.
"For the first time in a generation or more we will decide who comes to this country and, just as importantly, who does not", the defiant prime minister said.
"It's an option for the future, but it's not an option for today, because if we had a referendum tomorrow, what's it going to be on?"
The UK will now have a status that is more akin to that of Canada, Japan, and the United States, which allows for limited access to the EU financial market, but this can be modified if both the Britsh and European authorities agree.
Brussels, meanwhile, insists Britain can not have the same privileged access to the single market as it did as a member state after Brexit on March 29 next year.