Frontrunner Ms Truss has claimed there would be no new taxes or energy rationing if she became prime minister, as she dropped further hints about cost-of-living support this winter.
She added: “I will also deliver immediate support to ensure people are not facing unaffordable fuel bills. I will be robust in my approach. But it isn’t right to announce my entire plan before I have even won the leadership and got my feet under the table.”
Regulator Ofgem has confirmed an 80% rise in the energy price cap, which will mean the average household’s yearly bill will go from £1,971 to £3,549 from October.
Former chancellor Mr Sunak, who has repeatedly acknowledged he is the underdog, said “we shouldn’t rule anything out” on energy rationing.
He also sought to paint himself as the candidate offering a more realistic assessment about the way to approach the economy, with tax cuts not expected immediately if he becomes leader.
Mr Sunak said leadership “starts by being straight with the country about the economic challenges”, adding: “I’ve not chosen to say the things that people may want to hear, I’ve said the things I believe our country needs to hear.
“Although it hasn’t made my life easy, it is honest and, for me, that is what leadership is all about.”
He went on: “My plan is the right plan to tackle inflation, to compassionately support those who most need our help and to safeguard our children’s economic inheritance.
“Because as Margaret Thatcher and Nigel Lawson knew, maxing out the country’s credit card is not right, it’s not responsible and it is certainly not Conservative.”
Speaking at the 12th and final leadership hustings at Wembley Arena, Ms Truss also replied “yes” when asked if she would stop smart motorways amid safety concerns.
Voting in the Tory leadership contest closes at 5pm on Friday and the winner will be announced on Monday.
Mr Johnson and his successor will then go to Balmoral for the appointment of the new prime minister, rather than Buckingham Palace.
A palace spokesman confirmed on Wednesday that either Ms Truss or Mr Sunak will be meeting the Queen in Scotland, rather than in London as is tradition.
The Queen will receive Mr Johnson on Tuesday September 6 at her Aberdeenshire home, where he will formally tender his resignation.
This will be followed by an audience with the new Tory leader, where she or he will be invited to form a government.
The news will inevitably heighten concerns about the health of the 96-year-old monarch.