Marlborough District Council says good progress is being made in reducing the water level of a dam near Seddon.
There were concerns about the stability of the Haldon dam after Friday's big earthquake.
The council on Monday issued a warning to people living nearby.
Contractors are digging a trench so water can drain from the dam.
Mr Wheeler said he hopes the risk of the dam breaching will have gone by Tuesday evening.
However, he is still asking residents below the dam to be prepared to evacuate should something go wrong.
Residents still shaking since quake
A number of residents in rural Marlborough are struggling to cope after the magnitude 6.6 earthquake on Friday.
Support groups say people are suffering from sleep deprivation due to the regular aftershocks and the loss of many of their household possessions.
Seddon vicar Dawn Daunauda and her husband, who have been visiting people, said although they appear resilient, many are also very stressed.
Mrs Daunauda said it does not take much for some people to become tearful, for instance, when they hear that there could be another big earthquake.
Marlborough mayor Alistair Sowman does not think people who have left Seddon as a result of earthquakes will have left the area permanently.
The majority of houses in Seddon have some form of damage.
Mr Sowman believes that around 30% of homes in the area are vacant, but people will slowly start to come back when the quakes ease.