Finance Minister Philip Hammond on Sunday criticized the supposed plotters, arguing it would be "self-indulgent" to try to switch the leader.
Proposed by opposition Labour lawmaker Yvette Cooper and supported by more than 30 lawmakers, including Conservatives, it calls on the government to set out by the end of March 28 - if parliament has not approved May's deal by then - how it will ensure Britain does not leave the European Union on April 12 without a deal.
An effigy of British Prime Minister Theresa May passes by Downing Street during a Peoples Vote anti-Brexit march in London, Saturday, March 23, 2019.
The crisis talks started amid reports in The Sunday Times, The Telegraph and The Daily Mail about an imminent Cabinet coup. Lawmakers voted down the Brexit plan twice, and May has raised the possibility of bringing it back a third time if enough legislators appear willing to switch their votes.
Ms. May has had a tumultuous few days since returning from a summit of European Union leaders last week in Brussels where she enraged some leaders by appearing inconsistent about her Brexit plans.
Barclay admitted a series of indicative votes planned in Parliament would not be binding and could be ignored by the government. She survived a vote of no confidence at the end of last year, which means she's safe from a leadership challenge until December, but bettors anticipate a second vote of confidence in the government this year [1.33].
He told BBC One's Andrew Marr Show: "What Parliament has done is vote for a number of contradictory things so we would need to untangle that but ultimately, at its logical conclusion, the risk of a general election increases because you potentially have a situation where Parliament is instructing the executive to do something that is counter to what it was elected to do".
Conservative Party legislator George Freeman, a former policy adviser to Mrs May, tweeted that the United Kingdom needed a new leader if the Brexit process was to move forward.
"I'm afraid it's all over for the PM".
"Our first preference is to remain and the best way of achieving that is to have another referendum or to revoke Article 50", she said. But across the country you can see the anger.
It's been a week of errors for May, who made another hollow speech on Wednesday night, in which she assured the public she was on their side, before blaming parliament for the deadlock that saw her deal rejected on two occasions.
Gareth Rae, 59, who travelled from Bristol to attend the demonstration, told Reuters: "I would feel differently if this was a well managed process and the government was taking sensible decisions. We need a new PM who can reach out and build some sort of coalition for a Plan B".
Since the Brexit vote in 2016, the prospect of a second referendum has gone from something once barely imaginable to something remotely possible.
Marchers were lead in chants for a "People's Vote now" and many wore yellow fluorescent stickers reading "Bollocks to Brexit".
"Even after they leave, assuming they leave with a Withdrawal Agreement, they will spend two or three years consumed about what the future relationship is going to be like". The march, organized by the People's Vote campaign is calling for a final vote on any proposed Brexit deal.
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