The future of two community hospitals in Wiltshire will now not be known until July when the public consultation period ends.
Kennet and North Wiltshire Primary Care Trust says it may have to close the hospitals in Devizes and Malmesbury because of a �10m budget deficit.
It also says the nature of the service they provide has changed.
As many of the patients are elderly and most in need of rehabilitation, one proposal is to replace the hospitals with private nursing homes which include a number of dedicated NHS beds.
Two maternity units are also threatened with closure if too few mothers use the facilities.
BBC Health Correspondent Matthew Hill told News Online: "Staff here are hopeful that they can sell the message that the units are underused.
"They want to spread the word to patients further afield to come and use the facilities."
In February, more than 500 people protested in Devizes against the closure of the maternity units.