"What's happening here is not a shifting of red lines", Rory Stewart, the prisons minister, told BBC Breakfast.
"I don't think that there is any mileage for the Prime Minister or the Government in trying to do a deal with Labour because they will just try to trap Theresa May", he said at a launch event at Westminster.
Writing her response to his letter of last Wednesday, Mrs May told the Labour leader: "It is good to see that we agree that the United Kingdom should leave the European Union with a deal and that the urgent task at hand is to find a deal that honours our commitments to the people of Northern Ireland, can command support in Parliament and can be negotiated with the EU - not to seek an election or second referendum".
In a letter to Tory Party chair Brandon Lewis, the activists said any attempt to work with Labour to secure a deal or renege on manifesto commitments would be "catastrophic" for the party and lead to "severe electoral defeats" in the forthcoming May local elections. Treasury Chief Secretary Liz Truss yesterday refused three times to say whether she would remain in the Cabinet if a customs union became official policy.
Asked if May thus realised she needed more Labour votes, Stewart said: "Certainly, the maths suggest that to get this through we're going to need support from all around the house".
"I absolutely do not think that should be our policy", she told Sky News on Sunday. There are clearly two different positions - there are people who are more on the no-deal side, and people who are more on the customs union side.
May's letter came amid a growing presumption that while she remains officially committed to putting a revised Brexit plan to MPs as soon as possible, in practice this is unlikely to happen before the end of February, if not later.
In her letter, Mrs May said she wanted discussions between Tory and Labour teams to start considering "alternative arrangements" to the backstop contained within the withdrawal agreement.
Later on Monday, the Brexit secretary, Stephen Barclay, will go to Brussels to meet the EU's chief negotiator, Michel Barnier, following the PM's meetings in Brussels last week.
Mrs May does not agree, and wrote: "I am not clear why you believe it would be preferable to seek a say in future European Union trade deals rather than the ability to strike our own deals?"
She said the existing Political Declaration - the part of the Brexit deal setting out the goals for the future UK-EU relationship - "explicitly provides for the benefits of a customs union - no tariffs, fees, charges or quantitative restrictions across all sectors and no checks on rules of origin".