Residents in Dumfries and Galloway were given two days notice that their waste collections were being postponed before the bank holiday weekend.
Some residents must now wait weeks for their next collection.
One resident said that she was told that her general waste bin would be collected in a month, meaning that she is now having to use her recycling bins to store general rubbish.
She said: "It's either that or it gets left on the street and is going to end up everywhere because I'm not paying for it to be uplifted privately when it should be uplifted by the council.
"I'm lucky with just having one child in the Easter holidays but for people with larger families, it must be a nightmare for them.
"The bin men are entitled to their holidays on Friday and Monday like everybody else is but it's up to the people above them to sort that out and they really need to have picked another day for the bins to be uplifted."
A spokesperson for Dumfries an Galloway Council said: "All relevant staff chose not to work over the bank holiday weekend, and at this time have chosen not to work overtime to deal with any associated backlog.
"We informed the public as soon as we knew about the situation and will continue to work to find a solution."
In recent years, the refuse teams have worked on both Good Friday and Easter Monday.
The Labour Group Leader Archie Dryburgh said: " This is a complete failure and we demand answers.
"The Labour Group are seeking support from other groups on the council to call for an emergency full council meeting so that elected members can get to the bottom of this debacle."
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