In a speech on Tuesday, Royal College of Physicians president Prof Jane Dacre will warn ministers the issue must be addressed if their policy is to work.
She will highlight research that shows vacant posts are not being filled and gaps in rotas are being seen.
It comes as ministers are locked in a dispute with junior doctors over their plans for improving weekend care.
Last week thousands of medics went on strike over the government's decision to impose a new contract on them, designed to make it cheaper to rota on staff at weekends.
Prof Dacre will raise her own concerns at the RCP's annual conference in Harrogate, saying NHS trusts are struggling to find enough staff to cope with existing demands.
Physicians are doctors who focus on diagnosis and treatment as opposed to surgery. They cover a whole range of areas including stroke and heart disease to the care of the elderly.
Research by the RCP showed last year there were just over 13,000 consultant physicians across the UK - one in four of all consultants.
But four in 10 vacant posts advertised last year went unfilled, while one in five consultants reported gaps in their junior doctor rotas.
Meanwhile, one in 10 consultants say they often have to carry out junior jobs to ensure patients' care is not harmed.
Prof Dacre will tell delegates: "I feel sorry for NHS trusts, I really do. Across the country, they have created a raft of new posts to meet the rising demands for patient care, only to find that there is no-one to fill them.
"If we have neither enough trainees nor consultants to run the service now, how are we going to implement a safe seven-day service?"
She will go on to set out the case for extra funding, pointing out hospitals are racking up deficits and that funding lags behind other countries such as France and Germany.
"It is time to revisit our national contribution to healthcare," she will say.
But a Department of Health spokeswoman pointed out extra money was being invested during this Parliament - Â£8bn more by 2020.
She said this would help "make sure the right staff and support is available to create a safe NHS seven days a week".
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There are not enough doctors to run a seven-day NHS in England, according to a leading doctor.