They did it in Massachusetts. A report on the first national health referendum.
"Shall the Commonwealth of Massachusetts urge the United States Congress to enact a national health program which: provides high quality comprehensive personal health care including preventive, curative and occupational health services; is universal in coverage, community controlled, rationally organized, equitable financed, with no out-of-pocket charges, is sensitive to the articular health needs of all, and is efficient in containing its cost; and whose yearly expenditure does not exceed the proportion of the Gross National Product spent on health care in the immediately preceding fiscal year?"
D006076:Government; D008404:Massachusetts; D009310:National Health Insurance, United States; D013219:State Government; D014481:United States