More than 80,000 houses are included in the plans
Bill Speirs, the general secretary of the Scottish Trades Union Congress (STUC), attacked Labour over its backing for plans to transfer the city's stock to a housing association.
And he said the party would have fought the proposals "tooth and nail" if they had been brought forward by the Tories.
A referendum is being held over the proposals to transfer the local authority's housing stock to the not-for-profit Glasgow Housing Association (GHA).
The council and the Scottish Executive have argued that the move is the only way to pay for the work which is required on the buildings.
Under the proposals the city's £900m housing debt would be cancelled and GHA would be allowed to raise money privately.
However, opponents fear the transfer will eventually lead to big rent rises for the city's 80,000 tenants, who started receiving their ballot papers last week.
Speaking at a conference on Sunday, Mr Speirs claimed that a "yes" vote would lumber tenants with responsibility for sorting out "Glasgow's housing mess".
Council homes
He alleged that £5m of public money was being spent on advertising the campaign.
And he said: "Frankly, if Michael Forsyth and the last Tory Government had come up with this con, the Labour Party would be fighting it tooth and nail."
Mr Speirs said the executive was backing the move because it wanted to see the problems passed on to those living in council homes.
He said ministers would rather do this than have the council, the executive and the Westminster Government deal with it.
Tenants have three weeks to cast their votes and the result will be announced on 5 April.