The leader of Stockton Council said a fellow councillor caught drink-driving should "seriously consider her position".
Cllr Bob Gibson believes resignation could be an option for Lib Dem Julia Roberts after she received a driving ban at Teesside
The ward councillor of Bishopsgarth and Elm Tree was banned from driving for a year and fined £200 with £43 costs after being caught driving over the limit on
Cllr Gibson said: "I think she should consider her position very seriously and consider the people who elected her and how they will feel about it.
"With all the campaigns around at this time of year against drink-driving, I think councillors, of all people, should not be finding themselves in this sort of position.
"It's now up to her and the Lib Dems what she does."