The centre in Moreton is one of three Wirral Council considered shutting as part of the authority's £109m budget savings over the next three years.
Director of adult social care, Graham Hodkinson, said the council had no option but to close the facility on Pasture Road.
Campaigners say they will fight to save the Moreton centre.
More than 15,000 people have signed a petition against plans to close one of the three centres.
The other two were in Heswall and Eastham, which the council say are now safe from the threat of closure.
Mr Hodkinson said the council spends £6m a year on adult day services including transport, which he said was considerably more than similar sized authorities spend on social care.
He said: "We have to deliver these services more cost effectively."
Mr Hodkinson also said the reason Moreton was put forward for closure was due to its size, design and location.
He said the authority wants to deliver services for people with disabilities in smaller settings rather than large day centres.
Sally Anne Walton from Tranmere has a 41-year-old son, called Colin, who has autism and uses the centre.
Ms Walton said she was angry at the closure and worried about the implications for her son's mood swings if it closes.
She said: "I'm sure there are other ways they can save money rather than picking on vulnerable people.
"Emotionally and physically it would be very hard for Colin get to the other centres."
The centre will not close until a public consultation ends on 5 June.
As well as cuts to social care, the authority is axing 350 posts and has asked staff to take five days of unpaid leave a year as it tries to reduce costs.