Was it true universal healthcare? Was it a single payer system or something with private industry? Why was it politically stopped?
Politics, plain and simple.
Until the end of his life Sen. Edward Kennedy said his greatest regret during his political career was turning down President Nixon's deal on healthcare.
[This column] (http://washingtonpost.com/wp-dyn/content/article/2009/08/27/AR2009082703919.html) from 2009 and [this one] (http://bostonglobe.com/opinion/2012/06/22/stockman/bvg57mguQxOVpZMmB1Mg2N/story.html) from 2012 do a good job explaining the plan and the dynamics of the 1970s that caused it to fail.
The plan was not true universal healthcare, but it would have been a step towards universal coverage and possibly single payer.
What failure to make a deal came down to was interest groups lobbying Congress and throwing their electoral weight around. Once elections were on the line, elected officials chose not to risk those groups support next election.
I think those two columns only touch on, but do not really emphasize Ted Kennedy's prominence during these years. JFK was assassinated in 1963 and RFK in 1968, Ted Kennedy was the heir to the Kennedy political dynasty and heir to the party's Presidential nomination. Despite not being his party's official Senate leader, as the favorite for the nomination in 1972 he was in many ways the de facto party leader.
If Ted Kennedy agreed to a deal he would have brought with him Democratic votes in the House and Senate. Once Kennedy turned down the deal due to lack of union support there was nobody in a position to pickup negotiations. Unions made up a significant portion of Democratic voters and donors and no Democrat around 1970 would want to put that at risk, especially after it caused Kennedy to step away from the deal.