Politicians plan to stage a vote of no confidence in the leader of Bristol City Council over the appointment of a councillor who was later jailed.
The motion could leave the council without a leader
Members want council leader Barbara Janke to apologise for selecting former councillor John Astley, or they will put forward their motion on 28 October.
Astley was convicted of election fraud and downloading child pornography.
The Conservatives threaten to back the Labour motion if the Liberal Democrats do not find a solution to the problem.
The outcome could leave the council without a leader.
A new administration
Cllr Janke said the Labour move was "nothing more than a political game".
She told the BBC: "If I was kicked out then it would be the responsibility of the political opponents to form another administration."
Astley had served as a Liberal Democrat councillor for the Lawrence Hill area of the city.
Last month he was sentenced to five months in prison after pleading guilty to 11 charges of electoral fraud.
He was already serving a 19-month jail sentence after pleading guilty to offences involving child pornography.
At the time, Cllr Janke issued a statement saying: "We totally condemn his conduct."
Cllr Peter Haymond, Labour leader at the council, said: "She has indicated very clearly in public questions that she basically accepts no responsibility on behalf of her party for what happened.
"That, we think, is unacceptable."
Cllr Peter Abraham, Conservative leader of Bristol City Council, said: "Unless Barbara Janke and the Liberal Democrats come forward with some news of how this can be resolved we will back Labour."