The BBC's political editor Laura Kuenssberg said it was the PM's task to show she could "change the conversation" and demonstrate that Brexit would make a positive difference to people's lives at a time when her future was an "open question" within the party.
The British PM Theresa May appeared on the final day of her party's conference in Birmingham, dancing on ABBA's Dancing Queen, launched an attack on what she called the Jeremy Corbyn party, and she said that Britain is not afraid to leave European Union with no deal, but it will be hard for both sides.
One leave-backing cabinet minister told the Guardian that May was a "vehicle for Brexit", and she was likely to step down shortly afterwards; another suggested the optimal time to replace her would be in 2021, a year before the next general election is due.
Mr Rees-Mogg banged the same drum as Mr Johnson, demanding the Prime Minister scrap her Chequers deal much to the delight of the rank and file.
In her crucial keynote speech to the Conservative conference in Birmingham on Wednesday, Mrs May said next year's post-Brexit Spending Review will set out a programme of increased investment in public services, as a mark that the decade of cuts following the financial crash is coming to an end.
But Mr Dodds told ITV's Robert Peston the idea would not work - despite rumours Britain is prepared to make concessions to get closer to the European Union position.
"The fact that she didn't mention the word Chequers at all is an acknowledgement of the massive feeling against it", he said. Once more May did not provide any additional details about how the ruling party is going to implement these principles in action.
"We need to negotiate on something based on the Chequers proposals", he said.
Mrs May said she was lifting the cap on councils borrowing to fund new developments, in a move which aides said could lead to additional investment of an estimated STG1 billion ($A1.8 billion) in as many as 10,000 new homes a year.
She also tried to return to the message she gave when she was appointed prime minister in 2016, promising to help those who feel "left behind", many of whom voted to leave the European Union in the referendum of that year.
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"We must show everyone in this country that we are that party".
Theresa May speaks during the Conservative Party Conference in Birmingham.
May then set out a wide-ranging vision for the future, attacking leftist Labour leader Jeremy Corbyn, promising new homebuilding measures and vowing to make the economy work for those "left behind". But she refused to rule it out, adding: 'The resilience and ingenuity of the British people would see us through'.
"It is also the only deal that keeps the United Kingdom together, that avoids hard infrastructure on at border between Northern Ireland and Ireland or - even worse - a border down the Irish Sea". Many Conservatives expect her to face a leadership challenge soon after Britain leaves the bloc - or even before.
"We need a strong leader and we haven't got that at the moment", Duddridge told the BBC.
"Back business. Back them to create jobs and build prosperity".
"It is no surprise that we have had a range of different views expressed this week", she said.
In an upbeat passage in her speech, she will say: I passionately believe that our best days lie ahead of us and that our future is full of promise. Delivers on the issues they care about.
Ian Blackford, the SNP's Westminster Leader, said: "The Prime Minister danced around the key issues - the disastrous impact of Tory austerity and a Tory hard Brexit".