There is just one problem with this. A decision has already been made, not by the people but by the cabinet.
It is true that a slight hiccup has occurred in the shape of English Heritage, who are recommending that the Central Library should be listed as a building of architectural merit. But few believe the Government will take that suggestion very seriously.
Mullaney has set a hare running that has nowhere to go other than into the pantheon of urban myths in Birmingham. Enthusiasts for John Madin's 1973 brutalist Central Library will for ever accuse the council of failing to adopt the "visionary" Tate Modern plan, but the truth is that nothing really exists other than a few back-of-the-envelope jottings published on a website by Mullaney after he first thought of the idea sometime last Sunday.
The fact that his idea has taken off in the blogosphere simply underlines the plight of Central Library supporters who are now grasping at straws in their desperation to save the building so memorably described as an incinerator by Prince Charles.
One can only begin to imagine the fury of Tory council leader Mike Whitby, who has championed the Centenary Square library plan which he regards as one of the city's most important regeneration projects. Whitby, presumably, is under the impression that the Lib Dem half of the ruling council coalition agrees with him.
Certainly, Lib Dem deputy council leader Paul Tilsley has said nothing publicly to indicate anything other than unequivocal backing for both construction of the Centenary Square library and demolition of the Central Library.
But Mullaney is a strong-minded maverick who cares little for collective responsibility, even though he is chairman of the transportation scrutiny committee and as such part of the payroll vote and a member of what might be termed the Government of Birmingham.
What will be worrying Whitby about this episode is the fact that Mullaney is voicing publicly the fears that a few Lib Dem councillors, and some Tories, have expressed privately about the future of the library and Paradise Circus. Discontent has been festering away ever since the cabinet released details of the Centenary Square Library business plan, the details of which were ripped to pieces by a scrutiny review group.
The group held several meetings and was sharply critical of what it saw as a poorly thought through plan on an unsuitable site.
Oddly enough, the review group has no plans to publish a report putting together its findings.
Here's how Mullaney puts it: "I have always been up-front and honest. I don't agree that the Central Library should be demolished and I think you will find there are a lot of councillors, both Liberal Democrats and Conservatives, who agree with me.
"The figures for the Centenary Square library don't stack up and we would be shoehorning it into a tight site with no room for expansion."
The council was letting it be known last night that it regards Mullaney's proposal as an unnecessary distraction.
A decision has already been taken about where the new library should be built and that is that, apparently.