Attorney General Geoffrey Cox is in talks with EU officials on changes to the Irish backstop clause - seen as the sticking point for many Tories - which could tie the United Kingdom to EU customs union until a permanent trade deal has been agreed.
The prime minister is expected to put her Brexit deal before parliament for a second time by March 12 and will need the support of some Labour MPs to deliver it in the face of stern opposition from many Conservative backbenchers.
Speaking to Channel 4 News, the MP for Leave-voting Wigan said: "I think it's been so badly handled, this whole episode, that it's possible that Theresa May has lost even more trust than she had before, and that actually it will cost her votes rather than gain them".
They want to examine any agreement Attorney General Geoffrey Cox reaches with Brussels over the Northern Ireland backstop - to ensure it is temporary. "What's unacceptable is the mechanism", said the official.
Mr Cox had earlier poured cold water on the claims about his demands being dropped, describing then as "misunderstood fag ends dressed up as facts".
Britain is due to leave the European Union on March 29 - the first country ever to do so - but British lawmakers have rejected a draft deal sealed by May and her European Union counterparts in November.
I don't want to break our manifesto promise with talk of delays and another referendum, nor do I want to see the horrors that crashing out without a deal would inflict on the poorest in our society.
Britain now has tariff-free access to European Union markets and it benefits from EU trade deals with other countries.
'My conversations with senior diplomats and politicians from across Europe have given me cause for optimism that a breakthrough is near, ' he added.
Some members of the cabinet told the Telegraph they are not optimistic about winning the second meaningful vote as changes secured by Cox are not felt likely to win round hard-Brexit supporters in the party. But EU rules require border checks with countries outside the common market. "Our absolute focus should be on working to get a deal and leaving on 29 March".
"Communities across the country voted for Brexit as an expression of their desire to see change - that must be a change for the better, with more opportunity and greater control", she said.
She said: "Brexit or not we should be supporting funding to address the concerns of our towns and also the disparity between spending in the South and North on areas like transport".
On Tuesday evening, the First Ministers of Scotland and Wales joined together to tell the Prime Minister her "reckless" behaviour over Brexit "must stop now".
"The council has asked to be given all of the relevant documents in good time to consider them properly, in order to form a judgment in advance of a vote".
With 23 days left until Brexit and fears on both sides of the English Channel that an abrupt divorce without a pre-negotiated settlement could spell economic turmoil, the European Union is now nudging London to delay its departure.