Senior figures within Labour-led councils have warned party colleagues who are considering walking away from the Convention of Scottish Local Authorities (Cosla) to "put up or shut up".
At a crunch meeting today it is understood Renfrewshire Council leader Mark MacMillan will face pressure to stand down as Cosla's Labour leader - in theory the party's most senior councillor in Scotland - if he intends to lead his authority out of the organisation.
West Dunbartonshire, Dumfries and Galloway, Inverclyde and West Lothian will also be warned by some Labour figures that walking out of Cosla will hand their political rivals in the SNP carte blanche to push through whatever policies they see fit, with withdrawals giving the Nationalists total control within the body.
If they all leave, Labour would control only eight of Cosla's remaining 24 authorities, having held the balance of power since the 2012 local elections.
Inverclyde has already held discussions about reversing its decision and is expected to stay on the basis of some changes to Cosla's constitution.
It comes on the back of a letter sent to all Labour-led councils by Glasgow's leader Gordon Matheson, who has been leading the revolt, informing them that, along with Aberdeen and South Lanarkshire, Glasgow has now disengaged and will not attend the meeting.
Glasgow, which claims Cosla's funding distribution denies it about £15 million, will brief three of the rebel councils on its alternative to Cosla plans in the coming weeks. It plans a meeting with Renfrewshire.
A formal notice to quit has already been submitted but has a year's lead-in period.
All three will have paid annual subscriptions for Cosla membership for 2014/2015, totalling about £600,000.
One senior local government figure said: "It's fair to say the wheels have come off Glasgow's attempt to de stabilise Cosla. The Glasgow alternative model to Cosla seems to have hit the buffers big time, with councils showing no appetite for it whatsoever."
A senior source in one Labour council added: "It's incompatible that Mark MacMillan can stay as Cosla Labour leader if Renfrewshire is walking.
"Why would you walk away? All you're doing is playing into Alex Salmond's hands, leaving Labour in local government weakened while centralisation isn't going away soon.
"The fall-out from the police and fire centralisation shows the need for there to be a challenge. And what if boundary changes come on to the agenda? Where does that leave the smaller councils outside Cosla?"
One Labour council leader added: "There's every chance Mark will be challenged for the leadership in June. Or Renfrewshire could be gone by then. It's a difficult time at this point but I think we'll get through it. I'd prefer we united together."
The row has centred on where the power lies within the organisation, how funding to local authorities is distributed and the overall effectiveness of the body.
Cosla president David O'Neill, himself a Labour councillor, said: "I do not want to see this in terms of a battle with winners and losers. What recent events have shown me is that some of our member councils were obviously unhappy with some of our practices. I have listened to these concerns and acted upon them."
Mr MacMillan was unavailable for comment.