Brexiteer leader Andrew Bridgen has urged Ms. May to attend the Wednesday meeting of the Tory 1922 expert committee or risk losing more support.
Mr. Bridgen told The Mail on Sunday: "This week, Theresa May will discover that she is drinking in the lounge of the last opportunity and the bad news for her is that the bar is already dry.
"If it does not reach 22, that will make the letters come in even faster."
Former Brexit secretary David Davis also harshly criticized the prime minister and said he "managed to anger not only the defectors but also the fiery remnants."
Writing in the Mail on Sunday, he added: "We must not allow ourselves to be intimidated by the EU."
Reports suggest that up to 46 letters of no confidence have been sent to Ms. May.
These would be only two of the 48 needed by conservative parliamentarians to trigger a vote of total confidence.
However, Brexit's secretary, Dominic Raab, dismissed the threat to Ms. May's position and asked the party to join as a "team" to obtain the "best deal" for the United Kingdom.
Mr. Raab said: "I think it is understandable that there is nervousness on all sides of this debate and we have to keep our nerves going."
"The end is in sight in terms of a good agreement, the prize we want, a good agreement with the EU and I think colleagues should wait and see what it looks like.
"We do not want to return something that we do not trust is good business for the United Kingdom.
"But now is the time to play for the team, I think that's the way we get the best deal for the EU and I think that's what the country expects from us."
Sir Keir Starmer, Brexit's secretary of the workforce, also intervened in the "divided" party of the prime minister, criticizing his approach to the Brexit negotiations.
He said: "I do not think anyone thinks that this 30-year civil war at the Tory party in Europe is going to end before Christmas.
"What we're going to see is that even if there's an agreement, the Tory party will try to break it next year, some are already saying they're going to do it, so this idea of a historic moment just before Christmas in the national interest It will not happen, they will not stop fighting for this.
"We have reached the grave situation in which people say," Is this government really capable of fulfilling it because it is so divided? "