A number of Conservative MPs say they have submitted motions of no confidence in the Prime Minister in written letters to the 1922 Committee.
She told Sky's Ridge On Sunday that as far as she knew the 48-letter threshold for letters of no confidence needed to start a leadership battle had yet to be reached.
She said: "We fought that, we stood our ground, we said no, we're the United Kingdom, actually we can have a better more ambitious relationship with you".
More than 20 lawmakers have said publicly that they have submitted a letter, but others are expected to have done so confidentially.
"The focus is going to be on getting the deal into a better place". Two Cabinet ministers and a handful of junior government members resigned, and grumbles about her leadership erupted into a roar.
After the most tumultuous week of her premiership, which saw senior ministers quit over the draft divorce deal agreed with the EU, Mrs May said she would be heading to Brussels for talks on the "future relationship".
Mrs May herself will personally oversee the last 10 days of negotiations with the European Union on the future framework of relations, while Mr Barclay will focus on the domestic readiness for Brexit and getting Mrs May's draft withdrawal agreement through parliament.
Asked by Ridge whether she had considered stepping down, May said: "No, I haven't".
Tom Watson says it is time for Labour to be given a chance to rescue Brexit as he called for a General Election amid turmoil at the heart of Government. A relatively managed no-deal in which both sides acknowledge their inability to sign off a deal, and try to minimise chaos for businesses and people by reaching ad-hoc side agreements in important areas like border controls and cross-border finance contracts.
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But for the UK's embattled prime minister, it's now all war and precious little peace.
If May loses that vote - which there is no guarantee that she will - there will be a leadership contest in the Conservative Party to decide who will take over her position.
Mr McFadden said: "The real problem isn't who is the Prime Minister but what is the reality of Brexit compared to the promises made two years ago?"
The wider Tory rebellion follows the resignation of Brexit secretary Dominic Raab shortly after May's deal was revealed to MPs on Thursday, as well as the exits of work and pensions secretary Esther McVey and six other MPs and officials.
He suggested he would support a deal like that struck by the prime minister if it addressed those concerns. Brexiteers in her own party blame her for the withdrawal agreement, saying she has reneged on her promise that "Brexit means Brexit" and isn't following through on the results of the 2016 referendum.
It warned that leaving the European Union without a deal on trade and other relations - a path advocated by some Brexit supporters - "is not an acceptable option" and "would badly damage our economy by disrupting supply chains, causing shortages, and preventing vital services reaching people".
Dudley North MP Ian Austin said: "My priority is to get the best deal for Dudley so I want to see an agreement which helps local businesses and protects jobs, safeguards employment rights and the environment and has a proper plan on immigration". Reiterating the main points of the draft Brexit accord, she maintained that "the course I have set is the right one for our country". The current line from Brussels is that the deal can not be re-negotiated.
May is determined to fight on, warning that abandoning her Brexit plan, with Britain's withdrawal just over four months away on March 29, would plunge the country into "deep and grave uncertainty".