Dr Peter Bennie, chairman of British Medical Association Scotland, said figures claiming that doctor numbers are at a record high are not relevant when there are vacancies across the country.
NHS debate led to heated exchanges at First Minister’s Questions last week.
Nicola Sturgeon suggested struggling accident-and-emergency units in England should look to Scotland but came under attack from the Tories and Labour over the SNP’s stewardship of the NHS north of the border.
Dr Bennie told Sunday Politics Scotland: “We’re running vacancies right across the country - urban, rural, hospital, GP.
“And we’re just fed up with a mantra that says from the Government we have more doctors than ever before.
“The point is we need more again in order to be able to provide the service that people require.
“The relevant question is do we have enough doctors, do we have enough nurses, do we have enough staff outside the health service to provide the care that people need? And at present, we don’t.”
He added: “We’re stretched pretty much to breaking point, just trying to keep things going.
“If you take the situation with consultant vacancies, we have consultant posts vacant for over six months that are advertised that can’t be filled.
“Basically what happens with that is that all of the other staff - consultants and other doctors and nurses - are taking on more work to try to keep things going.
“The majority of staff in the health service are working way beyond what they’re actually supposed to be doing just to keep things running.
“And eventually that leads to personnel breakdown and eventually it leads to system breakdown.”
Scottish Labour health spokesman Anas Sarwar said: “This is an incredibly serious warning from the BMA.
“It is painfully clear that the SNP’s failure to properly workforce plan has left our NHS staff over-worked, under-valued and under-resourced.
“This has left our NHS struggling to cope with demand, and in the grip of a workforce crisis.
“A decade of SNP mismanagement has increased pressure on staff in every part of our health service - from nurses who say their workload is getting worse, to GPs who say their surgeries are understaffed.
“SNP cuts to social care are also adding more pressure to the primary and acute sector.
“Labour will not support an austerity budget and will instead offer amendments to the budget to use the new tax powers of the Scottish Parliament to stop the cuts.”
Health Secretary Shona Robison said: “We recognise that change is needed and last month published the Health and Social Care delivery plan to set out the actions and timescales to support healthcare professionals, charities and patient groups.
“It recognises that we must up the pace of change if we’re to deliver modern, sustainable health services and that local health boards and integration partnerships have an important role to play in taking this forward over the next year and beyond.
“By the end of this parliament, we’ll have increased health funding by almost £2 billion and delivery of the plan will be supported by record levels of investment in our health and care services - with extra resources for the NHS and for social care - plus dedicated funding of over £125 million in the coming year to help deliver change on the ground.
“NHS Boards have a statutory duty to undertake workforce planning. There are now 11,500 more staff working in our NHS, with nearly 1,000 of these recruited in the last year.
“Consultant numbers are also at a record high: in the last 10 years we’ve seen a 45.8% increase in medical and dental consultants, with vacancy rates held at the same level despite this huge increase in numbers.
“And since September 2006, NHSScotland nursing and midwifery staff have increased by 4.2%, or by 2,377.9 WTE as of September 2016. These extra staff will ensure people all across Scotland get the high-quality NHS services that they rightly expect.
“We are also committed to preparing our NHS workforce for the future by increasing student nursing and midwifery intakes for the last four years. That’s helped to see almost 10,000 nurses and midwives in training in 2015.”