The former Labour MP and MSP issued a stark warning for his party as he launched a new book, Scotland: The Growing Divide.
He said voters would back independence in 2014 unless Labour and the other pro-UK parties guaranteed far greater devolution by making it an option in the referendum.
Warning against a "self serving" battle between parties wanting the status quo or independence, he added: "The Scottish people have indicated they want a scheme that allows Scotland to stay in the Union but see the Union change and see far more fiscal, economic and other powers coming to the Scottish Parliament.
"But at the current time the Unionist parties are not listening.
"They are offering constitutional jam tomorrow and that's not credible. The people are ahead of the Unionist parties in embracing devolution – and the parties would be foolish to ignore what the people are saying."
Mr McLeish uses the book – a follow up to his 2007 analysis, Scotland: The Road Divides – to argue strongly for a second question on greater devolution appearing on the referendum ballot paper.
Labour and the other Unionist parties are opposed to the idea but McLeish said: "If there is not serious consideration given to a second question people will do one of two things – vote for independence or not vote at all.
"It will not work if Unionists say, 'We don't want a second question but trust us to deliver more powers anyway.' No-one is trusting politicians."
Mr McLeish – who advised the SNP Government on prison reform – warned time was running out for the party he led in Scotland from 2000 to 2001.
He praised Johann Lamont's leadership of the party in Scotland but added: "Labour is still struggling to get to grips with post-devolution Scotland. The 2007 election was a wake-up call but since then we have had five wasted years.
"I'm perplexed by that. As a party member for 42 years and as someone active in politics for 30 years I've not known a time when Labour has been so reluctant to embrace change and embrace the ideals of the Scottish people."
He criticised his party for having an obsessive fear of the SNP, adding: "Labour need to do two things – they need to be a progressive left-of-centre party but they also need to embrace Scottishness."
Mr McLeish also said Labour needed to stop thinking the Scottish electorate "owe us an entitlement" to rule.