Up to 1,400 Dumfries and Galloway Council staff are still waiting for back-pay some four months after a first deadline on their wage agreement.
Finance officers have said there is no guarantee the outstanding money can be paid next month.
Conservative councillor Gill Dykes, part of the administration, said staff were understandably upset.
Opposition Labour group leader Ronnie Nicholson said it affected low-paid workers and had become a "fiasco".
The hold-up has been partly blamed on the demands of introducing a new pay-roll system.
However, the news of the latest missed deadline has been criticised by both members of the Tory/Lib Dem administration and their political opponents.
Ms Dykes said those involved had every right to be upset.
"There is not one of us who wouldn't have been upset by the fact that we hadn't been paid," she said.
"We have given a deadline and now we are being told that the chances of meeting the deadline are slim.
"We need to do everything we can to make sure our staff are looked after properly".
She said staff in the human resources and pay-roll departments had worked hard to try to alleviate the problem.
However, she said they had not been able to do that.
"We need to be more sure of our facts before we move forward with these huge projects which affect everybody's daily lives," said Ms Dykes.
"There will be staff out there who are really unhappy they have been given one promise after another.
"Not only are they unhappy, but members are as well - we had no idea it was in this situation."
'Lot of mistrust'
Mr Nicholson said workers had been given "promise after promise after promise".
"Last year they were told they were going to get paid in March, then April, then July, it has just been a complete fiasco," he said.
"It is some of the lowest paid workers that have actually booked holidays on the strength of getting back payments."
He said the ultimate blame had to lie with the ruling Tory and Lib Dem group on the council.
"The administration just sit on their hands," he said.
"They haven't been looking after the employees, this is creating a lot of mistrust."