Doctors are calling for social services to be given more time to help tackle bed-blocking.
If the new Community Care Bill comes into force this spring, local authorities could be fined for each day a person stays in hospital when no care home place is available.
The British Medical Association (BMA) says social services departments need another year to see if recent Government investment leads to improvements.
Brighton and Hove City Council could face a fine of £1 million a year while in East Sussex it might rise to £2.5 million.
West Sussex, which has a large elderly population, is expected to have to pay out more than £1 million.
There are fears the departments will be penalised for some problems over which they have no control, such as a shortage of trained care workers.
Andrew Dearden, chairman of the BMA's community care committee, said: "We are already beginning to see improvements in some areas where social services departments have been able to use the extra funding effectively.
"This bill would place further financial pressure on already stretched local authorities.
"Delayed discharge is a major problem in our acute hospitals which causes distress to patients and relatives.
"The proper funding of community care, together with a multi-agency approach, is central to the success of the resolution of the bed crisis."
The number of bed-blocking patients in hospitals run by Brighton and Sussex University Hospitals NHS Trust averages between 90 and 100 and has a knock-on effect on services such as non-emergency operations.
Hospital bosses are working closely with Brighton and Hove social services to tackle the problem. This includes providing extra support to potentially vulnerable elderly people to stop them having to be admitted to hospital in the first place.
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