The TV star called on anti-EU MPs to "grow a pair" and replace Theresa May with a new leader who actually believes in Brexit.
But Mr Raab, who quit as Brexit Secretary over the PM's deal, insisted that holding a leadership contest now would be a "political parlour game".
The pair clashed on ITV's Good Morning Britain as the Brexit deal debate in Parliament entered its second day.
Mr Raab insisted that he only wants to defeat the withdrawal agreement – but still backs the PM.
But Piers hit back: "We know – you know, I know – Theresa May is not a strong leader. She's had her chance, she's been faffing around for a year now.
"Why are so many Tories right now, given this utter turmoil, why are you still persisting in this ridiculous public position that she's the only person that can lead the country at this time?
"Why don't you all grow a pair and put one of yourselves in charge and actually deliver the Brexit you keep banging on that you want? One of you – do something!"
The top Tory replied: "I think the public would regard it as political parlour games for us to be engaging in a lot of that shenanigans rather than just focussing on the deal.
"I also think the Prime Minister has every right – and this is why I stepped down – to present her deal."
Mr Raab insisted he is a "straight talker" – but then refused to say whether or not he'd stand to be leader if Mrs May did get forced out.
Mr Morgan said: "I can't for the life of me understand what is stopping the Brexiteers now, at this moment, actually saying 'Enough, we need one of our own and we need someone who can lead this country properly.'
"Why are you all defending this woman who looks to me completely defeated?"
Yesterday the PM suffered one of her darkest days as she lost three crunch Brexit votes.
She could lose her job within a week, with MPs set to vote on her proposed deal next Tuesday.
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