Former Cabinet Minister Priti Patel accused the Prime Minister and Chancellor Philip Hammond of “negativity” as they attempt to lead the country out of the European Union.
Ms Patel, who quit as International Development Secretary in November over undisclosed and unauthorised meetings in Israel, told The House magazine the Government needed to articulate a “better vision for the future” after Brexit.
Hedge fund boss and Tory donor Crispin Odey went further and called for Mrs May to be replaced by Environment Secretary Michael Gove to see the country through the negotiations.
Mr Odey told the Observer the Prime Minister could not make decisions and would not see Brexit through.
Their interventions came as Mrs May’s Government faced increasing pressure to find a workable and swift solution to deadlock over customs and the Irish border.
Mrs Patel told The House that the Conservatives had become “lazy” and she heard “too much relentless talking down” of Britain’s economy.
Asked if having two Remain voters at the top was part of the problem, she said: “I have to say, originally I thought it wasn’t. But I think it’s fair to say that there’s something in that. There is absolutely something in that.
“I actually resent the negativity.”
Talking about the wider Government, she added: “We are basically now at that two-year anniversary mark.
“Being bogged down in the minutiae is one thing. But moaning about Brexit in government and saying that it’s too difficult and talking down our country I think is actually quite shameful.”
However, she said that the party leadership should remain in place, adding: “They’ve got to deliver for the country. It’s non-negotiable.”
Mr Odey said Mr Gove should take over at the head of a much bolder administration that was prepared to break EU rules before Brexit.
He told the Observer: “Michael has got lots of attributes that make him a non-traditional Tory. He is very aware that he has to appeal not just to the wealthy, but also more broadly.
“I don’t think May can carry Brexit through any more.”
On Saturday, International Trade Secretary Liam Fox admitted Cabinet ministers analysing one of the potential solutions to the Irish border problem had met just once in the month since they were given the task.
The working group analysing the “customs partnership” proposal that would see Britain continue to collect tariffs on behalf of the EU was waiting for a report to be finished and will meet for a second time next week, he told the BBC.
A second group is considering Leave-backers’ favoured technology-based “maximum facilitation” - or “max fac” - solution.
Brussels has already rejected both schemes, with chief Brexit negotiator Michel Barnier saying on Friday that neither was “operational or acceptable”.
The Government has been told by EU leaders and Irish Taoiseach Leo Varadkar that they want to see progress over the impasse on the Irish border by the time the European Council meets at the end of June.
Tanaiste Simon Coveney upped the ante on Saturday, telling the Irish Times the UK must produce “written proposals” for the border within the next two weeks.
Meanwhile, civil servants have reportedly been drawing up scenarios for a “Doomsday Brexit” that would leave the country short of medicine, fuel and food.
The Sunday Times said this included models for mild, severe and “Armageddon” reactions to no-deal exits.
It quoted a source as saying that even the severe scenario saw the Port of Dover “collapse on day one”.
A spokesman for the Department for Exiting the European Union rejected the claims, adding: “A significant amount of work and decision making has gone into our no deal plans, especially where it relates to ports, and we know that none of this would come to pass.”