He really is caught between a rock and hard place
He can't sack her because internally he doesn't know if it will trigger a leadership election and it would be considered to be caving in to Labour and the LibDems and giving them a point in some mythical table. Also if he does sack her, even if it doesn't lead to a leadrship election it will still lay bare the absolute mess the Tories are in internally.
Labour and the LibDems are in a win / win situation because they've called for something that would be popular and when Sunak doesn't do it, partly because they called for it, makes the Tories out in yet more bad light.
She really is the gift that will keep on giving as far as opposition parties are concerned.