Jacqui Thompson faces a £190,000 legal bill and could lose her home after a failed libel case with Carmarthenshire chief executive Mark James.
Councillor Alun Lenny urged the council to settle the case, but his motion to discuss it at Wednesday's full council meeting has been refused.
The council said the "notice of motion as submitted was inadmissible".
Ms Thompson was removed from a council meeting and arrested in 2011 when she refused to stop filming it and was sued by Mr James over posts on her blog.
The council was granted a charging order which means Mrs Thompson could be forced to sell her home in Llanwrda, near Llandovery, if she cannot pay her debt.
Plaid Cymru's Mr Lenny submitted a motion asking that no-one be made homeless.
The council said: "The chair of council has confirmed that he ruled the notice of motion as submitted was inadmissible, because it did not meet the criteria set out in the council's standing orders."
A long-running legal row between a blogger and a council chief executive will not be discussed by councillors.