Time is running out for Theresa May. Though today's headlines concentrate almost exclusively on the prime minister's promise of more funding for the NHS after we leave the European Union, the row over the terms on which we will leave is boiling over in the background.

Speaking to Andrew Marr this morning, May confirmed that the white paper that will outline in detail the government's vision for our relationship with the EU after Brexit will not be ready until mid-July at the earliest, after the cabinet meets at Chequers to rubber-stamp it.

"In the week beginning 9 July we will publish a white paper which will set out, in more detail than the speeches any of us have given ... we will set out in more detail the ambition we have for the relationship with the European Union in future."

In other words, a full picture of what the government wants from Brexit won't be ready long after the prime minister meets the leaders of the EU27 at the European Council at the end of this month, the point at which David Davis hoped it would be ready, and just two and a half months before its summit in October, which to all intents and purposes is the EU's deadline for a deal.

The date May hopes to see the paper published – and on current evidence it would be foolish to say it's much more than a hope – is just a fortnight before the six-week parliamentary recess begins on 24 July. If she cannot break her habit of putting off big decisions and overshooting deadlines before then, then the government is sleepwalking into very tricky territory indeed.

The cause of the delay is obvious one: there is not yet anything like agreement within the cabinet, let alone the dysfunctional ranks of the Conservative parliamentary party, over what that white paper should contain. Two sub-committees of a cabinet sub-committee are still haggling over which customs model the UK should adopt after Brexit, despite both having been dismissed as unworkable by Brussels.

Despite the small victory May has handed to Leavers with the extra cash for the NHS this morning, brokering compromise between her party's warring factions gets harder and harder as time goes on. Even if she manages it, Brussels is still likely to reject the solution: successfully negotiating with 316 Conservative MPs and the DUP isn't same as negotiating with 27 member states.

For that reason, May has made a habit of merely deferring painful fights with her ministers and MPs for the sake of preserving the Tories' illusory unity and the security of her own position, as we saw last week. But that means the eventual fight with the EU27 will be even more painful, both at the negotiating table and back among her own MPs at Westminster, where the gravity of the concessions the prime minister has avoided being honest about with Brexiteers will hit home hard.

In an appeal to rebels preparing for another fight with the government over plans to give MPs a meaningful vote on the final deal as the EU Withdrawal Bill returns to the Commons this week, Robert Buckland, the solicitor general assigned with ensuring the legislation's safe passage, told the Sunday Politics: "Brussels is where the action is."

The trouble with that line is that it's an aspiration, not a statement of fact. All the action is at Westminster, where the government's energy is being wasted on the vexatious litigation of Tory Brexiteers. The more time wasted here, the less time there will be to salvage anything other than a catastrophic Brexit – both for Britain and May.