Carruthers has told his leading players that redundancies are "inevitable" as the dispute between club and governing body continues.
Edinburgh stopped their Scotland players training with their international team-mates last week and transferred their registration to a sports management company.
Carruthers denied any breach of rules, claiming they are not obliged to release them until July 13, but the SRU reported the case to the International Rugby Board.
The move saw the financial dispute hit a new low, with Carruthers preparing for legal action over an alleged six-figure shortfall in the SRU's payments to the club.
Carruthers claims McKie threatened to close Edinburgh down if they took the matter to court - and he has now warned his leading players they may have to look for a new club.
That prompted an angry response from McKie, who told the Sunday Herald: "After everything that has gone on this week, we no longer feel obliged to act the part of the undignified governing body.
"We simply cannot allow our preparations to be disrupted by this kind of thing. Bob Carruthers' actions are a real cause for concern, and we have to deal with that."
McKie claimed Carruthers could not make any player redundant. "The way their contracts are written means he can't just release them," McKie said.
"Most of them would be entitled to a year's salary at least. He's just trying to hold them to ransom by issuing these threats, but you can't just ignore employment law."
Carruthers has been phoning player's agents to update them. "I told them 'if your man has somewhere else to go then tell him to take it'," he said.
"I can't keep writing cheques on the blind. With great regret, I have to say redundancies are inevitable.
"We can't all be Barcelona - if we're Stirling Albion then that's great.
"We are determined to stay in professional rugby. It's not the vision we started with. But there's not a lot we can do about that, given the threats against us."