Brexit: Defiant words from PM may not be enough

She didn't budge. And she was never going to.

After her embarrassment yesterday at the hands of EU leaders, with restive backbenchers at her back, Theresa May was never going to use this highly unusual appearance in Downing Street and dramatically reverse out of her position.

Simply, to back down less than 24 hours later would have looked weak.

And the prime minister has invested huge amounts of time, effort, and political capital into her Chequers plan.

Ministers never believed that it would be the precise form of the final agreement.

But Number 10 believed that in good faith, they had put something credible on the table for discussion.

She has already lost two cabinet ministers over the compromise, and endured weeks of attacks from different wings of her party.

So one, albeit, highly embarrassing diplomatic bust-up was not going to force her to back down.

Her anger was visible though today, explaining again why she believes the two familiar post-Brexit trade options, Norway and Canada, cannot, and will not work for the UK.

And she called for respect from the EU: "Throughout this process I have treated the EU with nothing but respect, the UK expects the same".

A stern tone, strong words.

And in going further on citizens' rights too, perhaps Mrs May has sought to take the high ground, in contrast to what some in the UK are seeing as the EU's poor behaviour yesterday.

But while there is no remote sign from the PM today that she is about to compromise, forces in the EU and in her own party are intent on forcing her to do so.

Her problem is that they want to push her in different directions.

Rhetoric doesn't change the fact that few of the players involved outside Number 10 believe that the suggestions the prime minister has put forward can be the ones that ultimately will win the day.