One option under consideration includes closing 24 libraries across Kirklees, leaving just the main libraries at Dewsbury and Huddersfield.
The council has discussed plans to cut the library budget from £6.3 million to 2.8 million. An investment of £1.4 million after cuts would see services still restricted but turned into hubs, or libraries would be kept open using volunteer groups. A public consultation will be held in the Autumn and final proposals made in February 2015.
Kirklees Council confirmed that in total £129 million will be stripped out of the council budget from 2010 to 2015, meaning £60 million will be cut from the council budget over the next three years.
Unison branch secretary Paul Holmes said the plan to close all but two libraries will see 100 jobs lost, while one of the other options could see 60 jobs lost.
He said: "Either way, if we don't watch it there will be no services left. Unison said it had now "had enough" and there would be a ballot for industrial action on August 8. Mr Holmes said the wide disparity of income levels across Kirklees meant running libraries through volunteers was unreliable.
Councillors suggested that services in Cleckheaton be reduced and moved to Spenborough Town Hall, Cllr Kath Pinnock (Lib Dem, Cleckheaton) said: "It's an ill-conceived idea.
She said: "Cleckheaton's library was purpose built to serve over 40,000 people, and there is no way that the building can close. Cleckheaton library is a Grade II listed building and offers many community services.
"We must work out how the money can be saved.
"Cutting library services suggests libraries are not being given the priority they deserve.
"Changes can happen without destroying what is built. Once libraries are gone they will not come back."
Cllr David Sheard (Lab, Heckmondwike), who chaired the meeting on Wednesday, said closing the libraries would be "awful".
But he said there was no easy answer and it was an extremely serious situation.
Cllr Andrew Palfreeman (Con, Birstall and Birkenshaw) said if possible the party did not want to see any libraries close. Cllr Palfreeman said he wanted to see decisions made from the "bottom upwards rather than up downwards."
He said volunteers were "welcome and necessary" but said plans to see them run libraries were unsustainable.
Councillor Steve Hall (Lab, Heckmondwike) said: "It's inevitable that some things are going to change. The fact of the matter is people don't go to libraries any more. We'll do everything we can to make sure libraries stay open."
Kirklees Council said anyone who would like to discuss this further should contact their local councillor.