How much progress has Theresa May really made on the Brexit deal?

What should the PM hope to get out of today’s working lunch with Jean-Claude Juncker?

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Will Theresa May face triumph or disaster or something in between when she sits down for a working lunch with Jean-Claude Juncker today?

Well, you pays your money and you makes your choice: the Telegraph and the Guardian both lead on the failure to make any headway on the question of the Irish border. The FT is more chipper, and there's an excellent long read on the accession talks by Alex Barker in that paper too. The Times has an upbeat assessment: "Brexit deal 90% there, says official" is their splash.

Of course, as everyone who has ever updated their computer knows, the progress bar can hover around 90 per cent for a very long time. Whether by accident or design – and I suspect when the papers are all in the public domain and the memoirs have been published, that'll be the debate that obsesses historians of the May government more than any other – the PM has got to a point where she has managed to sand off most of the biggest reality-defiant demands of the Brexiteers without the wheels falling off the wagon.

The problem is that the biggest and most unachievable of those demands – the United Kingdom out of the customs union and single market, no barriers between Northern Ireland and the rest of the country, but no physical infrastructure on the border between the Republic and Northern Ireland – is still unresolved. I'm not going to speculate on whether there is a form of words that can be cobbled together today that is (a) acceptable to the Irish government, (b) acceptable the DUP, on whom May now relies in the Commons, and (c) reconcilable with the objectives in the Lancaster House speech because we'll know that soon enough in any case.

But what should worry Theresa May and anyone hoping for a non-disruptive exit from the European Union is that while the PM has got this far without a major eruption, the signs about what's ahead don't look good. There is a lack of understanding among some Leave MPs and prominent commentators about what exactly the inaptly-named "divorce bill" is for and what it buys.

The United Kingdom is settling its accounts for payments it agreed to as a member, not buying a better standard of a trade deal. That is in any case largely set by the government's Lancaster House asks, which point to a low-access, high-freedom future relationship on the Canada model rather than a high-access, low-freedom relationship similar to that of Switzerland or Norway.

(It adds to the government's difficulties that some pro-Remain politicians are talking about the £50bn as a "cost of Brexit": no, whatever happens, the UK's outstanding liabilities would have either been paid as a member or as a departing member. Whether you stay in the restaurant with your friends or if you leave your share behind before you go, the bill does not change. Nor does paying your bill have any bearing on the quality of the taxi home or, in this somewhat overworked analogy, the final trade deal.)

That the government has done a non-existent-to-poor job of explaining all this and the trade-offs involved is one reason why sufficient progress may not be enough to prevent a failure of Conservative nerve later down the line. One of the repeated criticisms of May is that she triggered Article 50 without first hammering out what the United Kingdom's desired final end relationship would be with the EU. An equally big problem is that as well as keeping that conversation away from the cabinet, May has declined the opportunity to persuade her own party or the public what the final relationship should look like as well.

Stephen Bush is special correspondent at the New Statesman and the PSA's Journalist of the Year. His daily briefing, Morning Call, provides a quick and essential guide to domestic and global politics.