Nearly 70% of Scots strongly support a publicly owned national care service free at the point of need.
The poll, commissioned by the Scottish Socialist Party (SSP), found huge backing for the radical policy being funded by general taxation.
Care homes have been at the epicentre of the coronavirus crisis, with thousands of deaths being recorded.
The tragedy triggered a debate on the future of a service that is largely privately operated.
Unlike the NHS, which is free, in many cases residents have to stump up thousands of pounds for residential care.
The Daily Record, as well as figures in the SNP and Scottish Labour, have led calls for a national care service that is not based on profit.
The SSP, early champions of fundamental change in the sector, commissioned Panelbase to carry out a poll.
Over 1,000 people were asked if they agreed with a national care service free at the point of need, paid for out of general taxation, and which is publicly owned.
Those polled were asked to place their support on a scale of one to 10, where one is “not at all supportive” and 10 is “wholly supportive”.
A clear majority, 69%, put themselves at between seven and ten. The figure was 73% for women.
Fox said: “These figures bear out what the SSP and others, like The Daily Record, have been arguing for some time.
“The care system today looks like the health model was before 1948 when the NHS was established. Back then health services were provided by private doctors, provision was patchy and standards varied greatly. It was a health system not fit for purpose. That’s why our grandparents’ generation fought to change it.
“It is clear from this poll that the people of Scotland are unhappy with the current adult social care model. They want elderly care provided for everyone, paid for out of our taxes, publicly owned like the NHS.”
Labour MSP Monica Lennon said: “It is not surprising that people in Scotland support the creation of a National Care Service, free at the point of need.
“Scotland needs a new way of delivering social care that doesn’t undervalue workers. Scottish Labour will create a National Care Service that provides dignity for all.”
SNP MSP Shona Robison said: “The COVID-19 pandemic has reminded us of the vital importance of social care services, but it has also underlined the need for reform and improvement of those services – which is why the Scottish Government’s commitment to examining the idea of a National Care Service is welcome.
“That review must also consider the needs, rights and preferences of people who use services, their families, and their carers – and ensure that the voices of those with real life experience of the social care sector are heard.”