The current administration formed as a result of the SNP becoming the single biggest party after May’s local elections, with seven councillors.
But the LibDem and Tory groups, who have six councillors apiece, have regularly voted down the administration.
They recently teamed up to vote through a controversial motion to cut council employees’ redundancy terms.
A spokesperson for the SNP group said today in a press release: “Although the SNP is the largest party and running as a minority administration, the Tories and Lib Dems have more councillors combined - and they are plotting to grossly cut redundancy terms for local authority staff.
“The Tories and Lib Dems are also threatening to terminate staff contracts and re-engage them on new lesser terms and conditions if they do not accept what is offered.
“At the last meeting of the council, they voted to slash redundancy terms for local authority staff without any discussions or negotiation.
“With the trade unions having already suspended partnership working with the council in response to this decision, SNP Council Group Leader Gordan Low said that a vote at a council meeting tonight (Thursday, December 21) is the ‘last chance saloon’ and that the Tories and Lib Dems must ditch their ‘Scrooge’s scheme’”.
SNP Council Group Leader Gordan Low added: “The SNP group on East Dunbartonshire Council are not prepared to have this backward move imposed on the council staff - and we are standing firm with the trade unions, who have already utterly rejected this plan.
“As the SNP Scottish Government makes progress delivering fairer working practices, it is completely untenable for us to be in charge of a local authority that wants to drag down its own staff.
“For these reasons the Tory and Lib Dem councillors’ Scrooge’s scheme to slash workers’ rights must be ditched at the meeting on Thursday - or the SNP administration will tender their resignations at the end of the meeting.”