Staff at Musgrove Park hospital in Taunton have been told the NHS Trust cannot rule out redundancies.
Taunton and Somerset NHS Trust has to make savings of £6.5m in the current financial year - 4% of the total budget - but is short of that target by £1m.
Mike Williams, chief executive of the trust, said it was "still our ambition to avoid redundancies" but it could "no longer guarantee this".
Unions have advised staff to help find solutions to the current problems.
Mike Slade, chair of the Joint Staff Trade Unions, said: "We are committed to working in partnership with the management at the hospital and felt the staff had a right to be trusted with this information about the latest position."