Former British Foreign Secretary Boris Johnson has compared May's plan to putting the country's constitution in a "suicide vest" and handing the detonator to the EU.
"I think we should let the prime minister get Brexit over the line at the end of March and leave the longer-term debate about what our new relationship is to a new-generation leader".
"It is clear that the stories about an imminent challenge to Theresa May are still weighing on sentiment and the pound will find it hard to rally too far before more clarity on Brexit emerges", said John Marley at FX risk management specialist SmartCurrencyBusiness.
May will present her case to her European Union counterparts at an informal meeting in Salzburg next Wednesday, before the other 27 leaders discuss how to respond among themselves.
Similar proposals have been rejected by the United Kingdom government in the past.
Britain's Treasury chief said Tuesday that striking a divorce deal with the European Union over the next two months is "doable", while the boss of Jaguar Land Rover warned that tens of thousands of jobs could be lost if the country crashes out of the EU with no agreement.
Downing Street on Tuesday reiterated that Chequers was "the only serious, credible and negotiable plan which is on the table which both delivers on the will of the British people and which prevents the imposition of a hard border in Northern Ireland".More news: IPhone Xr Release Date & Pre-Order Details
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With just 200 days to go to the scheduled date of Brexit, Mr Baker said that the PM would lack credibility with Brussels negotiators if she tried to press ahead with her departure plan at the party conference without the backing of her party.
If a deal has been reached by then, it will need to be approved by MPs. British politicians inside May's governing Tory party, as well as in the opposition Labour Party, are preparing to sabotage the agreement.
Mr Baker, the former chairman of the Eurosceptic European Research Group, said Mrs May faces a massive problem because of the scale of opposition to Chequers among Tory grassroots members.
A number at the meeting said they had already submitted letters of no confidence in May, the source told the BBC.
Business groups and civil servants say a "no-deal" Brexit could cause disruption to shipping, barriers to trade with the bloc, a fall in the value of the pound and even shortages of essential goods. This outline of a proposal to Brussels sparked the resignations of her Brexit Secretary David Davis and Foreign Secretary Boris Johnson.
"Brexit is a negative negotiation, unfortunately".