Board members from the University Hospitals of Morecambe Bay, which runs hospitals in Kendal, Barrow and Lancaster, have discussed the financial challenges facing the trust.
They told the council's Health Scrutiny Committee that the trust has to deliver savings in line with government cuts and reduce their own deficit.
From a gross spend of £260 million, they need to deliver savings of £30 million by April 2014.
"It is not going to be easy - there will be anxiety and concern surrounding the savings".
However, Mr Bennet promised that for every service cut, medical directors would fully examine the impact on patients before the cut was made.