The European Research Group of pro-Brexit Conservative MPs, who are leading the challenge against May, believed the figure had already reached 48 letters on Friday.
So I'm absolutely committed to getting the Brexit that 17.4 million people voted for.
Andrea Leadsom, the minister in charge of government business in parliament, has told the BBC that she was supporting May but was not fully happy with the deal.
Mr Raab said Britain was being "bribed, bullied and blackmailed" to accept a deal which would keep the United Kingdom locked in the customs union with the European Union.
Our Brexit Insider Facebook group is the best place for up-to-date news and analysis about Britain's departure from the European Union, direct from Business Insider's political reporters. He said: "I only resigned on Thursday morning so I can't say I have had extensive conversations".
The last week in Westminster has been one of the most dramatic I can remember. They say that some lawmakers who were undecided about the call for a no-confidence vote could reach a decision after they met with their supporters over the weekend.
Writing in the Sunday Telegraph, Mr Goldsmith said that under the PM's plan "in effect, Britain would remain in the European Union, but without having any say".
He added: "Had that been the choice, I personally would have voted to remain".
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With mounting speculation that May could be forced out, few observers have been able to predict what might happen next as she has insisted that she has no plans to leave 10 Downing Street and is "determined" to see the Withdrawal Agreement go through.
"It has close to zero chance of making it through Parliament and with only five months remaining, we can not afford to waste any more time on it".
Simon Clarke, Tory MP for Middlesbrough South and East Cleveland, said today is a "crucial day" for the PM, telling his fellow lawmakers that "this must be the point at which action is taken".
Addressing the issue of immigration, a concern for many businesses who fear they will face skills gaps after Brexit, May will promise to introduce "more streamlined application processes" that will "attract the brightest and the best from around the world".
The Sunday Times also reported Britain's army had been ordered to step up contingency plans to help police maintain public order in case of food and medicine shortages after a "no deal" Brexit, citing an unnamed "well-placed army source".
We're saying to the government: "Get real, you've got to get real", the shadow chancellor John McDonnell told Sky News.
She will go on the attack over her Brexit plan on Monday, using a speech to say that the withdrawal agreement has been "agreed in full".
Whether or not Mrs May wins an improved future partnership offer this week, she still has to get the withdrawal deal itself past the Westminster Parliament.
"And it is our failure to make proper preparations that has so gravely weakened our negotiations". She then suddenly raised stakes, saying that "the choice before us is clear - this deal or leave with no deal".
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.