Mr Coleman, who is working as an advisor to Mr Smith and previously helped deliver the Olympics for Boris Johnson, said Mr Corbyn's challenger was better placed to deliver the economic policies proposed by Shadow Chancellor John McDonnell.
"However, a significant minority backed Owen Smith". "I would invest in a British New Deal ... a Keynesian investment programme for the healthcare, homes, schools and jobs".
The debate began with a clash on Europe and the European Union referendum, with Mr Smith accusing Mr Corbyn of poor leadership during the referendum campaign.
Jeremy Corbyn has been accused by his rival Owen Smith's team of travelling more miles in the first three weeks of his leadership campaign than he did during the two-month campaign to keep Britain in the European Union.
Confidence is twice as high amongst those that voted "Leave" compared to those that voted to "Remain" (72 per cent versus 35 per cent).
Mr Corbyn responded saying he was "saddened" by the vote and he did not want the United Kingdom to be a "bargain basement' island with low taxes and low workers rights".
"I won't do what Jeremy did and vote against my party 500 times".
"I will serve Labour on the backbenches because I'm Labour to my bones".
He said: "Other countries are plotting a more protectionist, introspective future for themselves and you want to work with them".
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But Mr Smith said the current tactics were reminiscent of the time the party was out of power for 18 years.
Insisting that Corbyn "cannot lead us back to power", Smith said Labour was at 26% in the polls, it's lowest in over 30 years, according to the BBC.
However, he said the Chilcott report into the Iraq War made "pretty sobering reading" and said he would preside over "a different, less aggressive foreign policy", if he became Prime Minister.
Mr Smith was among dozens of Labour MPs to resign from Mr Corbyn's front bench in protest at his leadership.
The shadow work and pensions secretary dismissed the plans as "rhetoric" which will not restore Labour's economic credibility around the country, especially in marginal seats.
Jeremy Corbyn's Labour is 13 percentage points behind the Tories, according to an opinion poll which suggests the public rates Theresa May more highly than the Opposition leader.
In contrast, Mr Corbyn gave his closing remarks to huge applause as he called for a new housing policy, re-nationalisation of the railways and a national minimum wage of £10 "that means something".
Smith has clearly realised that Europe is his strong-suit, and he went on the attack when asked how he felt on the morning of 24 June - describing himself as "gutted" with the result and "disappointed" that Labour hadn't done enough to win the referendum.