Earlier, a spokeswoman for May told reporters that a one-page document had been shown to lawmakers during meetings aimed at finding a way forward on Brexit.
He said that to get a deal that could get the backing of MPs, Mrs May had to "ditch the red lines and get serious about proposals for the future".
Under EU rules for a member state leaving the bloc "we will leave the EU without a deal on March 29 unless parliament either agrees a deal with the EU or the United Kingdom revokes Article 50 and chooses to stay in the EU permanently", she wrote.
With the Prime Minister appearing unwilling to budge despite the overwhelming rejection of her plan, MPs may take the process out of her hands in parliament next week. They are getting ready for another referendum.
The Telegraph has learned that a delegation of five ministers from the group visited the Prime Minister in No 10 and warned her directly that they were prepared to quit.
"These discussions brought to the surface the complete misunderstanding in government circles about the time line to bring it about", Liberal Democrats leader Cable said as quoted by The Guardian newspaper.
And Conservative chairman Brandon Lewis said: "I am disappointed to see Labour again yesterday trying to frustrate and avoid Brexit by hanging open that they would possibly go for a second referendum".
Mr Farage also reiterated his position that "Brussels isn't working" and claimed the Brexit vote had inspired other European Union countries to demand the right to "govern our own countries".
Ocasio-Cortez Uses Violent Sexual Term To Describe Her Far-Left Agenda
On Monday, Donald Trump dismissed pot-shots fired by Ms Ocasio-Cortez, after she called the president "racist". Ocasio-Cortez and Tlaib both identify as democratic socialists.
Mr Hammond said removing options had consequences.
"The fact that my team are willing to continue talking to her team of senior ministers this morning suggests that at least there is a willingness to explore these things", the Lib Dem leader said.
Ms Sturgeon responded in a tweet: "So everything is not on the table".
If he were in government, Blair said, "I would already be having discussions with Europe about the terms of extension".
In shunning the Davos meeting, which she attended past year, May follows in the wake of Emmanuel Macron, under heavy domestic pressure driven by gilets jaunes protests, and Donald Trump, who cancelled his visit due to an ongoing government shutdown in Washington.
Britain, which would face by far the biggest disruption, has devoted thousands of civil servants and several billion pounds (dollars) on measures to mitigate the worst effect - although officials can only speculate about what will actually happen on March 30 if Brexit happens without a deal.
He warned that Labour meant to hold another confidence vote "if necessary" as part of his bid for a general election that he says would resolve the impasse.
If May fails to forge a consensus, the world's fifth-largest economy will drop out of the European Union on March 29 without a deal or will be forced to delay Brexit, possibly holding a national election or even another referendum.
"We want to defend the interests of French fishermen, defend the interests of fishing areas, and companies that take part in this significant economic sector", he said.
May has refused to countenance another election, having lost her parliamentary majority in a snap poll in 2017 that left her reliant on the support of a small Northern Irish pro-Brexit party.