Having failed to sell her Brexit deal to MPs, Theresa May is now attempting to sell it directly to the country. Her chosen medium implies a certain degree of masochosim, as she is subjecting herself to a format she isn’t particularly good at, on a subject where her arsenal is very weak: radio phone-ins.

Last week saw the prime minister do Nick Ferrari’s show on LBC; today was the turn of Emma Barnett and BBC Radio 5 Live. The questions and answers more or less as one would have expected. Asked whether her deal could win the approval of parliament, May said she was in the business of persuading people, that she believed it delivered on the result of the EU referendum, that the EU would not offer anything better, and that its failure to pass would result in “division and uncertainty”.

This is the line that Downing Street hopes might induce some of the Brexiteers on its own benches to return to the fold and vote with the government – that a Brexit can only be certain if the deal is approved by parliament rather than rejected by a Commons where the majority of MPs are opposed to a no-deal scenario. But, almost in the same breath, May stressed: “There is no question of no Brexit.”

She’s right, of course – the only certainty in all of this is that, barring an withdrawal agreement being approved or parliament agreeing on an alternative course of action, the United Kingdom will leave the EU on March 29th 2019, with or without a deal. Which is itself the argument Downing Street is making to Remainers: voting this deal down risks a catastrophic no deal scenario. For reasons of party management and basic arithmetic it’s necessary for the Tory leadership to make each of those contradictory arguments to the two camps at once but one of the many reasons why this is not working is that, as May demonstrated, ministers are prone to make them both at the same time (or within the same answer) in public.

The interview was almost more interesting for what May didn’t – or couldn’t – say. She refused to say whether she would resign when the deal is rejected and floundered when asked whether it would be better than no Brexit at all, the line we are increasingly hearing from Tory opponents of the withdrawal agreement (most recently Dominic Raab), and refused to answer in the affirmative without heavy qualification. “It will be a different world for us outside the EU, but it will be a good one... I genuinely believe there is a bright future for this country and our best days lie ahead of us.” Hmm. That even the prime minister cannot convincingly rebut the argument that her deal is worse than EU membership – or even try – is a sign of why she cannot hope to get it past parliament.

Regardless of whether May managed to win over anyone listening, what matters much more is that her answers only add to the body of evidence Tory Brexiteers are using to justify not voting for her deal.