The claim, by Rory Stewart, comes as he launches his leadership bid on day two of the campaign, along with Andrea Leadsom and Mark Harper.
Mrs Leadsom is promising to tackle the climate change "emergency" and claiming she is an "optimistic yet realistic Brexiteer" who can restore trust in politics.
But frontrunner Boris Johnson, who has yet to stage his campaign launch, is attracting more backers, including former party leader Iain Duncan Smith and pro-Remain prisons minister Robert Buckland.
Mr Johnson was also the overwhelming favourite at hustings organised by the 92 Group of right-wing Conservative MPs, winning the support of 34 MPs, with 18 for Dominic Raab and six for Michael Gove and Esther McVey.
Mr Stewart's attack on his rivals follows spending pledges by leadership candidates including:
Mr Stewart declared: "We must restore - for Britain and for the Conservative Party - our reputation for economic and fiscal prudence. We simply cannot make spending and tax cut promises that we can't keep.
"This number - of total spending promises by other candidates in this campaign - is eye-watering. We have to be straight with people, truthful on Brexit, and truthful on spending.
"We cannot criticise Jeremy Corbyn for reckless spending pledges if we start doing the same ourselves. Cheap electoral bribes could cost us dear. Our members are smarter than this."
At her launch, Mrs Leadsom, who is proposing what she describes as a "managed exit" from the EU by 31 October, will outline a programme for her domestic agenda.
She will characterise her plan as "bringing our country back together, healing the divisions, building new homes, securing our streets, helping our businesses to thrive and achieving a carbon-neutral economy".
On climate change, she will say tackling the issue is not only right for the planet and for future generations, but also offers the chance to develop new "clean" technologies which could rival the UK financial services sector in size and stature.
She will outline her ambitions for a major expansion in housebuilding, to help young people get a foot on the housing ladder while providing new opportunities for those looking to downsize.
At the same time, she will stress her support for strong public services, including schools, policing and the NHS, while committing to a cross-party commission to deliver a solution for social care.
On the economy, she will promise "low taxes, incentives for enterprise and strong employment opportunities" while warning of the "existential threat" posed by a Labour government led by Jeremy Corbyn.
"Our party has thrived in the past, when it has governed as a champion of the people, providing freedom of choice and opportunity, a strong economy and global leadership," she is expected to say.
Describing what drives her in politics, Mrs Leadsom will cite her parents' divorce when she was four, and her mother and stepfather's later success opening a furniture shop in the 1970s in the face of a Labour government that "destroyed incentives".
At the same time, she will underline her commitment to the "diversity, compassion and opportunity" which make Britain the "envy of the world".
"Whether your life starts well and gets into difficulties, or starts with problems and ends in triumph," she will say.
"And whether you were born here and your parents and grandparents before you - or whether you or your parents chose to come here from elsewhere in the world to make this great country their home - every one of us has a stake in our shared future."
Announcing his backing for Mr Johnson, Mr Duncan Smith writes in The Daily Telegraph: "We have to leave the EU by 31 October or I fear the British people will finally leave us, once and for all.
"That is why I have decided to vote for Boris Johnson in the Conservative Party leadership election. I believe of all the candidates he is the most likely to deliver on the requirement to leave the EU by 31 October.
"He has grasped that imperative. While there are other good candidates standing, too many speak of how damaging this would be. How, I wonder, will the EU take their discussions seriously if they see frightened negotiators from the UK sitting in front of them?
"Boris has also made it clear that he believes that we should offer a trade deal and, while that is being negotiated, we should seek an implementation agreement with the EU under which we will both go to the WTO and invoke Article 24, which allows us to continue tariff free trade until the final deal is agreed.
"We can work urgently on our proposals for alternative customs arrangements to replace the backstop at the Northern Irish border prior to our departure.
"To do this we need leadership and Boris is, as he showed in London, capable of also capturing a mood of optimism for too long missing in our message to the electorate."