But the warning came as an NHS England report suggested 'decision support from a patient's own GP practice and hospital specialist nurse/team, seven days a week' could help solve the urgent care crisis.
The urgent care report by NHS England medical director Sir Bruce Keogh also proposed options including 'seven-day continuity of care from a patient's GP practice'.
The report, which acknowledges GPs are under 'considerable strain', calls for a simpler, better co- ordinated urgent care system.
Meanwhile, a prominent GP called for practices to operate on a 'never full' basis - never turning away patients during core hours - to ease pressure on A&E.
GPC chairman Dr Laurence Buckman told a Westminster Health Forum event on 18 June that he did not believe GPs would be forced to take back out-of-hours duty. However, GPs were likely to be involved in supervising the service, he said.
Dr Buckman said many GPs, including him, were working 'typically, a 12-hour plus day'.
'Many of us now perceive the hours we are working as dangerous. When I am in my 14th hour, I know I'm not thinking straight. I don't think patients deserve that.
'Many GPs, whatever the out-of-hours arrangement, will look after the terminally ill. But for everybody else there has to be a point where you stop working because it is not safe. I believe that point has been reached.'
His comments echo concerns in an RCGP poll of 258 GPs this month, which found 85% believe rising pressure has left them unable to guarantee safe patient care.
But Dr James Kingsland, clinical lead for the NHS Clinical Commissioning Community, said demand management by practices was the solution to pressure on A&E.
About 80% of urgent care demand is during GP core hours, he said.
'My practice is one of a number that says we are never full. In our opening hours, no patient is ever turned away - the number of calls made between 7am and 8am, to GP out-of-hours services, and between 6.30pm and 9pm, for a practice population of 5,000, is just one call every four weeks.'
Derbyshire LMC medical secretary Dr John Grenville called for more clarity on the urgent care proposals. He warned that one-to-one care by a named doctor 24/7 was not possible.