Labour’s Ken Edwards told a finance meeting that he was “very, very gloomy”.
“I think we’re crossing our fingers to avoid a S114 situation,” he said.
Meanwhile, Janet Clowes of the Conservatives, said: “We need to do everything in our power to avoid a 114.”
A section 114 notice is when a council cannot balance its budget and is effectively bankrupt.
In the event of such a notice, authorities cannot commit to any new spending and must come back with a new budget in 21 days, which can mean severe cuts to frontline services.
The authority has applied for exceptional financial support from the government.
During the meeting, Liberal Democrat Reg Kain said: “I want to know why exceptional financial support, which is going to still bring about the cuts that we’re going to suffer, is a better situation than a 114 because, from where I’m sat at the moment, I can’t see us really avoiding a 114 in the future.”
But Labour’s Jill Rhodes said that although exceptional financial support required the council increasing its borrowing, a S114 notice would require commissioners coming in.
“Those commissioners have to be paid by the council, and you lose political control of your council, it is run by commissioners,” she said.
“So, democracy is probably not best served by a 114 notice and commissioners.”
A number of authorities, including Birmingham and Thurrock, have issued section 114 notices in recent years.