St Helens Clinical Commissioning Group (CCG) in Merseyside could suspend all non-essential hospital referrals for four months during the winter.
The CCG's lay chair, Geoffrey Appleton, said the group recognises the move "won't be popular" but is facing a funding gap of £12.5m this year.
The British Medical Association (BMA) called the move "unacceptable".
The CCG, which was recently rated "inadequate" by NHS England, is also suggesting a two-year suspension of IVF services for people aged under 37 and stopping provision of gluten free foods and some over-the-counter medicines.
Mr Appleton said the plan would "support hospitals during the busy winter period" and allow them to concentrate on the sickest patients.
Explaining the group's situation in its Financial Recovery Plan, he said: "Imagine our NHS budget is your household budget and every year the cost of living goes up but your salary doesn't increase; the result is money becomes tighter and tighter."
"Now imagine another relative comes to live with you and because of their health needs are unable to work and cannot contribute financially. How would you manage?"
Dr Richard Vautrey, deputy chair of the BMA's GP committee, said the move "highlights the incredible financial pressure facing general practice and its impact on patient care.
"It cannot be right that the public will be effectively denied access to healthcare because the local CCG has run out of money," he said.
He called on government ministers to "step up their commitment to resolving this crisis".
"The cost to the health service of delaying referrals could ultimately be much greater in the long term as more complex and costly problems develop as a result".
The CCG says it is "under-funded" compared with other areas in Cheshire and Merseyside.
An NHS spokeswoman said deciding how to prioritise resources are "very difficult for commissioners" but CCGs must "plan and manage demand over winter".
"St Helens CCG is actively engaging with its local population on the best way to ensure patients have their care prioritised over the busy months for the NHS", she said.
Charity Coeliac UK criticised plans to cut gluten-free prescriptions, saying it "will leave vulnerable patients without support" and "could cost the NHS more in the long run".
The NHS England regional office will review the proposals before a decision is made because of the CCG's inadequate rating.
The proposals are under public consultation until 5 October.