During the debate, from Labour's Party Conference in Manchester, the former Home Secretary, Charles Clarke, said he thinks the prime minister should quit.
John Prescott and Charles Clarke
He said: "I'm very sceptical personally about his [Mr. Brown's] capacity to pull it round and therefore I do think he probably should stand down.
"But I don't rule it out. He's a man of great quality, he was a very good Chancellor of the Exchequer and of course it's entirely possible he might, but I am, as you rightly say, a sceptic about his capacity to do that."
But the former Deputy Prime Minister John Prescott accused Mr Clarke of sour grapes: "I'm all for the argument. I've got no problem about that. The Labour Party always has arguments.
"It's had the Blairites and the Brownites. Now we've got the "bitter-ites". Of course he's bitter. Charles knows that. I mean, Charles and I have been in the same room as Gordon and I've seen this kind of expression of bitterness. I'm sorry about that."
John Prescott whose defence of Gordon Brown was cheered
Mr Prescott and Mr Clarke were joined in the special debate by the Guardian columnist Polly Toynbee and a collection of Labour activists, trades unionists and experts.
The audience - comprising mainly of Labour party members - cheered as John Prescott gave a characteristically bullish defence of Labour's past policies, brandishing the famous 1997 pledge card.
He called on delegates to take the attack to the Tories, warning that any leadership election would undermine Labour's chances of winning another election.
Jon Sopel directed the debate
He said: "Be clear about it. You can't sign up for the fourth term and have six months rowing in the party. . Absolute nonsense. Absolute nonsense."
But Mr Clark, and others, warned that the party was at risk of sleep-walking into a defeat unless the problems are tackled head on.
He said: "I'm not talking about six months. And John's quite wrong on his timings. The point is what John is suggesting is: don't discuss the question - walk into a wall."
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