The Army should be drafted in and "pop-up wards" erected at Accident and Emergency departments where patients are waiting hours to be admitted.
The head of the union that represents Scottish ambulance staff also said "major incident" procedures should be initiated to increases resources.
Unite's Jamie McNamee said crews were waiting up to three hours in Glasgow and Aberdeen to hand over patients.
The Scottish government said 99% of calls were handled in under 30 minutes.
It comes after the head of the ambulance service apologised for waiting times.
Pauline Howie said staff were working under "unprecedented pressure" in response to a "huge increase" in Covid and non-Covid cases.
She said everything was being done to get people to hospital as quickly as possible, including hiring new staff.
But the Unite union said patients were being put at risk because ambulances were having to queue for hours outside A&E departments.
Convener Jamie McNamee said: "Regularly we have ambulances queuing at facilities throughout Scotland.
"A couple of good examples are Aberdeen Royal Infirmary and the Queen Elizabeth University Hospital in Glasgow where routinely crews will wait three hours."
He said NHS staff were "absolutely working their socks off", but that the average turnaround time for call-outs had far exceeded the 20-minutes it was supposed to take.
"Our first option would be to initiate internal national risk and resilience procedures. That would entail building or producing pop-up wards outside the A&E departments that are unable to cope with demand, allow the crews to hand over the patients to these trained clinicians and free up that mobile asset to respond to treble-nine calls," he said.
"I believe the Army would have similar facilities that could come in helpful. I'm sure they're busy themselves, however I think we find ourselves in a bit of a national crisis at the moment."
The Scottish government said the NHS was facing significant challenges as the pandemic continued.
A spokesman added: "Despite the pressure coronavirus has brought upon our ambulance service, which serves some of the most rural areas in the UK, in 2020-21 crews responded to over 70% of highest priority calls in under 10 minutes and more than 99% in under 30 minutes.
"It is vitally important there are no unnecessary delays for ambulances taking patients to hospital and we continue to work closely with the service and with health boards across Scotland to ensure ambulances are cleared as quickly as possible.
At First Minister's Questions Nicola Sturgeon said the average wait last week for immediately life-threatening incidents was nine minutes and 30 seconds, a figure she described as "not good enough".
Opposition politicians have cited incidents where patients have faced far longer delays, with Scottish Conservative leader Douglas Ross describing how a stroke patient in Dumfries waited 14 hours for the arrival of paramedics.
Several health boards across the country have warned of rising Covid cases putting severe pressure on their services.
NHS Highland said it was having to return to prioritising vital care and treatment, such as emergency admissions and cancer care.
NHS Grampian said Covid patients were up more than 40% in a week while NHS Fife, NHS Ayrshire & Arran and NHS Greater Glasgow and Clyde have postponed non-urgent surgery.
Health Secretary Humza Yousaf has previously warned the NHS was facing a "perfect storm" of pressure.
He said A&E services and ambulance turnaround were under particular strain.