Image copyright PA Image caption Tory MPs Iain Duncan Smith, Nicky Morgan and Steve Baker are all advocating the Malthouse Compromise

While Westminster is looking the other way, scouring the ranks for more defectors, don't forget the government is trying to press on with achieving what looks like the near impossible in Brussels.

That is, wresting enough concessions from the EU to give them a chance of pushing their Brexit compromise through Parliament so we can actually leave the union on time.

Attorney General Geoffrey Cox is working on the "Cox codicil", which the government hopes will be something tangible rather than just legal flannel, to tweak the backstop, the controversial clause aimed at preventing the return of a hard border on the island of Ireland.

And the prime minister herself is expected in Brussels this week, to get, ministers hope, a sense of what the EU's "best and final" offer to help close the deal will be.

Part of the political handling that, although clumsy, has got Number 10 this far, is consideration of the so called Malthouse Compromise (remember that?).

A process that has involved Conservative former Remainers and Brexiteers, chewing over what some of them believe is a genuine solution to the deadlock, and is, for some of its supporters, the only way the Tory party might get through this without smashing itself to bits.

The government has, for good political reasons, taken the proposals seriously, in the sense that they have hosted hours of talks between officials and the group, and tried to keep its participants' hopes up.

Remember, part of the reason the Brexiteers defeated the government last week was a frustration that the prime minister was not rushing to adopt the Malthouse Compromise.

But as the moment of the truth approaches, with the Brexit deadline getting closer, this act of political management now presents a dilemma in itself.

Image copyright PA

Although one Cabinet minister dismissed the Malthouse plan at the start as "another unicorn", an impossible fantasy in other words, senior figures in government now believe that some of the proposals that have been thrashed out with officials do potentially have merit.

In fact, whispers suggest some formerly ardent advocates of Remain have been rather surprised at the possibilities.

There is a big but, however.

Officials and ministers who can see the advantages of some of the ideas, and you can read more about Malthouse here, are equally clear that given the time constraints, they believe they can't provide a way out of the current problem.

One senior source said: "We're not rubbishing it, but it can't be a solution to the current problem."

Another insider said: "we need a way of concluding it."

There are, it's believed, ideas that could form part of the discussions in the next phase of the Brexit talks.

But there is, some government figures think, a need, sooner rather than later, for it to be made clear that the proposals can't provide an urgent fix to a very pressing political problem.

Having created an expectation, that is a dilemma in itself.

The core of the Brexiteer group are not people who enjoy being let down gently.

Depending what happens in the next couple of days, more urgent problems than that might come to the fore.

Several Conservative MPs are understood to be taking the idea of quitting the party altogether very seriously.

One of them told me they might not last the week.

Another said: "It's not exactly looking good."

If a number of Conservatives join former Labour MPs in a centre grouping, however loose, the idea of Theresa May being able to command a reliable majority becomes more fanciful still.