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.
"One of the reasons people voted to Leave was because they felt they were not getting a fair suck of the sauce bottle, as they say".
We are reaching the point now where it is extremely hard to see how we can rescue the Conservative Party from a catastrophic split if the Chequers proposals are carried forward, he said.
The biggest obstacle still to be resolved in the talks is the question of how to avoid customs checks and police at the border between Northern Ireland and the Irish Republic, once the United Kingdom has left the bloc.
Devolution could see Yorkshire become 'England's Catalonia'George Freeman, who was chairman of the Prime Minister's policy board until November past year, said he believed Mrs May should "seal the deal" before handing over decisions about the long-term relationship with the European Union to a successor.
"So I think it is extraordinary now that he is no longer in cabinet that he is taking such an aggressive position to try and undermine work that he was involved in as part of the British government". The rift deepened this week with Johnson comparing May's plan to a "suicide vest" on Britain's constitution.
"We have given him a jemmy with which Brussels can choose - at any time - to crack apart the union between Great Britain and Northern Ireland".
Communities Secretary James Brokenshire said he thought Mr Johnson had used the wrong "tone" in the article.
"I'm sorry, but this is the political end of Boris Johnson".
The flurry of activity came after Mr Johnson launched a fresh attack on the PM's Brexit plan, claiming it would be "substantially worse than the status quo" for British businesses. "If it isn't now, I will make sure it is later".
At a conference in the Alpine lake resort of Bled in northwestern Slovenia, Michel Barnier said a Brexit deal was "not far" and that some 80 per cent of the withdrawal agreement had been agreed.
"I did not sit down with a plan 20 years ago to become prime minister", he added. "Well I don't think he has".
The ERG has condemned May's plans for Britain to remain in a free trade zone for goods with the European Union after it leaves the bloc in March next year but has faced criticism itself for failing to suggest a detailed alternative.
TUC general secretary Frances O'Grady said: "Whether it's through a general election or a popular vote, Mrs May should take her deal on the terms of Brexit and put it back to the people".
While talk at Westminster is of the potential for a second referendum, MPs will consider the legitimacy of the 2016 plebiscite which resulted in the historic decision to leave the EU.
Andrea Jenkyns, who has submitted a letter of no confidence in May, told AFP the prime minister was "too dogmatic" to change course.