Wirral NHS Trust has announced a five point plant to cut a projected overspend of £6m.
The plans include closing a rehab ward for elderly people, introducing car park fees and admitting day patients instead of them staying overnight.
But a decision on the closure of wards six and seven at Victoria Central Hospital in Wallasey - which would save £2m pounds - is deferred until June.
The Transport and General Workers' Union has vowed to fight the closure.
'Funding changes'
Trust chief executive Frank Burns said: "The challenge we face at the moment is a consequence of a significant disparity between the additional funding we have received and increases in our operating costs.
"In the coming years the Trust will benefit from changes in the way it will be funded, but in the meantime we are duty-bound to ensure we make the very best use of the resources available to us."
A public consultation process has been taking place over the future of the wards at Victoria Central Hospital.
The decision on their future will be made by the respective Boards of Directors of Birkenhead and Wallasey Primary Care Trust (PCT) and Bebington and West Wirral PCT on 7 June.
Said Mr Burns: "We are confident that the right decision will be made to close these two wards which we believe are now surplus to our requirements as a consequence of the recent investment in transitional and intermediate care facilities."
But Dave Laird of the TGWU said the fight would go all the way to central governemnt to save the wards.
He added: "And if the government doesn't support us we'll go to a judicial review."