Here is a striking and singular thing.
Downing Street's director of Communications Robbie Gibb on Saturday "liked" on Twitter a tweet by Nigel Evans, the senior Tory MP, which says that Sir Graham Brady's and Andrew Murrison's amendment calling on the government and EU to dump the Ireland backstop would "empower PM in discussions with EU and give closure which is necessary to delivery the Brexit the people voted for".
In other words, this appeared to be Downing Street giving official approval to the amendment.
I wrote about the significance of the Brady amendment on Friday, and said that Brady and his fellow signatories - who include Evans - had hoped the PM would endorse it, and then force all Tory MPs to vote for it on Tuesday by enforcing a so-called three-line whip.
But the point is that what is being asked for in the amendment by Brady, Evans and their fellow members of the executive of the 1922 committee - the body that represents Tory MPs - is NOT government policy.
In the words of one minister, "the cabinet hasn't signed up for it".
Gibb seems to be signalling that the PM will endorse the amendment.
But she presumably will at least go through the motions of securing the rubber stamp of the Cabinet before doing so. Presumably.
And for the avoidance of doubt, and as I explained in my earlier note, the reason the Brady amendment is not government policy - or at least not yet - is that it could be a car crash, for two reasons.
First, if parliament were to reject an amendment gilded by the PM's imprimatur, all hope for her would then be lost of being able to persuade the EU that any changes to the Withdrawal Agreement and Brexit plan would secure the ratification of MPs. At that point the choice for the UK really would be a no-deal Brexit or no Brexit.
Second, even if Parliament did back the amendment, what it demands is so big and complex that the rest of the EU might respond by either saying "non, nein, never" or by saying that the change is so hard and complex that Brexit would have to be delayed for months - which the Tory MPs who drafted the amendment would say negated the whole point of their attempted compromise.
Again no-Brexit or no-deal would swiftly ensue.
Stakes are therefore high for the PM, in deciding whether to follow through on Gibb's endorsement of Evans's tweet.
There is a second significance to Gibb's social media sally.
It may confirm a shift in the balance of power within May's close circle, or at least that is what cabinet ministers tell me. The point is that Gibb favours maximising pressure on the EU to dump the backstop, while the preference of the PM's chief of staff Gavin Barwell has been to build a cross-party coalition for the PM around an alternative and softer Brexit.
Gibb as a director of comms has become an important political actor - almost perhaps with the clout within the court of Theresa May that Campbell had in Blair's. Gibb is wise enough to know powerful courtiers often meet a sticky end.