Dr Alan McDevitt, the new leader of the country's 5000 GPs, said his members cannot fit any other jobs into their 10-minute appointment slots yet still find time for the patient's own concerns.
He also warned that if the Scottish Government wants to do more to prevent elderly people from going in and out of hospital, the country would need more GPs and nursing support staff.
Practices are already turning round to hospitals and saying they cannot take on such work as extra follow-up blood tests for patients who have been discharged from the wards.
Dr McDevitt, chairman of the British Medical Association's Scottish GPs Committee, said: "GPs are under enormous pressures now.
"The consultation is saturated. There is not anything else you can squeeze out of it and still leave the patient's individual needs anywhere."
He said doctors were routinely calling up a patient's details on their computers during consultations only for the screen to be filled with appointment reminders.
"We have probably gone as far as we can with the remind system flagging-up," added Dr McDevitt. "You have to leave space for the patient and the problem they have come in with that day."
The Clydebank-based GP also said that, as patients were discharged earlier, surgeries were being increasingly asked to do the work of hospitals.
He said: "Most hospital letters we get back now will ask us to do something. Often the first thing people do when they get out of hospital is to phone us."
GPs play a greater role in diagnoses too. Dr McDevitt said that in the past consultants would send test results back to GPs along with an opinion about the patient's condition. Now, he said, the clinician would perhaps rule out a serious illness, such as cancer, but offer no other explanation for the symptoms, leaving the GP to decide on what to do next.
Dr McDevitt claimed the relationship between family doctors and hospital consultants was more distant than ever as they rarely saw each other. Passing on information about patients or treatments was more difficult, partly due to secretaries being replaced by pools of administration workers.
He said GPs would have to say no to taking on any extra work unless there was more capacity, which meant "more professional time, physical space in the building and other staff to help us".
Doctors were given a controversial new contract in 2004 which increased their income while allowing them to give up responsibility for out-of-hours community care. Since then, the number of doctors north of the Border has risen from 4456 to 4937.
However, policies such as moving responsibility for adult community care from councils to health boards are changing the landscape.
The chairman of the Royal College of General Practitioners (RCGP) UK Council, and the leaders of the GP Councils for Scotland, Wales and Northern Ireland, wrote a joint letter to health ministers across the UK earlier this year urging them to develop a co-ordinated national vision for the future of the NHS and patient care.
The RCGP said that GPs were "mission critical" to the future of the NHS, "particularly at a time when health services across the UK were being asked to find ways of delivering services more efficiently without compromising quality of patient care".
It called on governments to invest in general practice and build on its strengths –including providing more care in the community, hiring more GPs, giving them more time with patients and extending their training
A Scottish Government spokeswoman said: "GPs are central to meeting our nation's significant health challenges and we very much value the vital contribution they make.
"We are fully committed to supporting GPs to do what is best for their patients and on strengthening links between hospital and community treatment.
"NHS Scotland and the NHS Institute for Innovation and Improvement, in partnership with general practices, designed and tested an innovative programme, The Productive General Practice, which is now being used across Scotland to help GP practices reduce waste and streamline services."
The spokeswoman added that £325 million was being invested in community health premises through different initiatives.
Contextual targeting label: