The Taoiseach and the Tanaiste are expected to admit defeat in their support for the Nice Treaty at a press conference soon.
As no votes for the Treaty continue to come in from counting stations across the country, Mr Ahern and Ms Harney are expected to confirm that they have given up hope of the Treaty being passed.
The result has come as a major embarrassment to the Government and the main opposition parties, who had all supported the yes campaign.
A rejection of the Treaty will mean that Ireland will not be viewed favourably by its fellow EU members and will probably lead to a renegotiation of the Treaty.