You have the timeline wrong. Our march to socialized healthcare started in the 1930s when Blue Cross became a tax-free conduit for prepaid healthcare, and in the 1940s when FDR capped wages pushing employers to offer health plans as benefits.
What really needs to be done is to untangle employers and insurers from being preferred healthcare payment channels. The tax code is what makes it that way, and distorts the market through a pile of regulations gathered up over time. People can't afford health care on their own because the market is for large corporations to purchase in bulk from other large insurers who set the prices, and state legislators who target these large organizations.
This also brings up another problem. Making things tax-free to purchase with an income tax system means complicating the tax code, and making it more expensive to hire employees. A sales tax system would work better for such a situation, where you don't tax the people purchasing the product.
Exactly; the FDR programs were the large start of government interference with the private sector, and has grown through regulations/oversight, etc., to a complex tax code to cater to special interests' protection. This new "Socialized Medicine-Lite" that's coming will be the same as the "temporary income tax", that has grown, grown, and continues to grow, until it becomes strangulation of private competitors/market-based competition.