Two Primary Care Trusts wants to shut hospitals in Bradford-on-Avon, Devizes, Melksham, Savernake, Trowbridge, Warminster and Westbury.
West Wiltshire and Kennet & North Wiltshire Primary Care Trusts want to replace them with enhanced GP surgeries or 24-hour community teams.
West Wiltshire PCT is currently £7.5m in debt, and Kennet & North Wiltshire is more than £8.2m in the red.
Two health clinics in Devizes and Trowbridge are also under threat.
Carol Clarke, West Wilts & North Wilts PCT's chief executive, says that doing nothing is not an option.
"I would much rather work in collaboration with people to do what we need to do. Changes here are going to be made."
A public consultation on the plans started on 13 March and is due to last for 13 weeks.
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