Managers are seeking additional funding for a first-wave private finance initiative hospital due to open in less than five months' time.
Brian Waite, chief executive of Carlisle Hospitals trust, said patient services could suffer if the money is not found. He has appealed to North Cumbria health authority - which insists no more money is available.
Finance managers in Carlisle have confirmed that they need to find annual savings of£3.2m to finance the running costs of the new hospital, only£2m of which has so far been identified.
About£420,000 of the shortfall comes from unexpectedly high annual business rates for the£67m new hospital.
Finance director Gordon Hendley said that when the full business case was signed, the trust was proceeding on the basis that business rates would be£380,000, the same as on its existing estate. But the business rate for the new hospital will be£800,000.
Mr Waite said: 'It is unfortunate, but nobody had advice or guidance on the business rate issue.
'We are moving to the new hospital from 1 April and there is limited time to resolve this financial issue. We need support from the HA and regional office to deliver the hospital everybody wants.'
Mr Hendley said: 'There are basically two options - either reduce services or run up a big deficit, neither of which is acceptable. We have to find a solution.'
The problems came to light after a leaked HA document showed that an extra£7m was needed to set up and run the new hospital. This includes a oneoff£750,000 for demolishing a tower block at Cumberland Infirmary,£2m for joint running costs and£2m to cover variations to the PFI scheme.
Northern and Yorkshire regional office has agreed a bridging loan for building variations. The trust is still in negotiations over the demolition and joint running costs.
Robin MacLeod, chief executive of North Cumbria HA, said: 'They are looking to the HA and regional office to bail them out, and we have already given them all the money we have for this purpose. They are going to have to make sure their hospital stacks up to what was in the original contract.'
Unison regional official Peter Doyle said: 'The hospital was originally held up as the cheapest option, but it is a disgrace the way money has been poured in to this scheme secretly. What we are left with is a smaller hospital and service reductions.'