Councillors at North Somerset Council have voted not to accept a single directly-elected "Metro Mayor" for the West of England.
Four West councils, including Bristol, South Gloucestershire and Bath and North East Somerset, were offered the deal in the Chancellor's March Budget.
They would receive £900m over 30 years to invest in key areas such as roads.
However, North Somerset Council's Conservative leader Nigel Ashton said the deal is "not attractive enough".
He said: "We have worked hard with our fellow West of England partners to get the best available deal for the area, but too much remains that we are not prepared to support".
He said the money offered would have to be borrowed, with around £400m spent on interest rates.
Mr Ashton also said any future "resources or powers" would be controlled autonomously by the proposed mayor leaving the local authorities "with no say in it whatsoever".
He added that if the plan went through, what remains of local government in the region would "wither on the vine".
The other three councils in the West of England are due to meet on 29 June to decide whether to accept the deal or not.
As North Somerset rejects the move, the other councils would need to renegotiate.
Bristol City Council and South Gloucestershire Council have indicated that they support devolution, while Bath and North East Somerset Council has not yet stated a preference.
If approved the councils would come under a new authority called the Western Powerhouse and receive £30m a year as part of the devolution deal.
"Metro mayors" are local government executive leaders who have been directly elected by the people who live in a local authority area.