Most voters do support universal healthcare, Medicare for all, and single payer, and since 2016 support has grown significantly. https://www.kff.org/slideshow/public-opinion-on-single-payer... More recent polls show slightly higher support.

But whether people would support a specific plan that has a new payroll tax(and greatly reduces premiums, deductibles and copays, and still saves the government hundreds of billions each year) and all but abolishes private insurers is less certain. This is part of the reason why Biden's plan is for a new government insurance plan, not single payer or "funded" through a payroll tax. But it does include some provisions of S.1129 - Medicare for All like the start of lowering the medicare age