Megan McCardle at the Atlantic looks at the Gallup polls then and now:
Now, Medicare popularity did improve after it passed. On the other hand, it wasn't passed despite terrible polling, with a controversial process, by a political party that was tanking in popularity thanks to a grinding recession.
Nor was Medicare partisan.
Summary of Party Affiliation on Medicare Vote 1965
SENATE
YEA NAY NOT VOTING
Democrats 57 7 4
Republicans 13 17 2
HOUSE
YEA NAY NOT VOTING
Democrats 237 48 8
Republicans 70 68 2
Source: http://www.ssa.gov/history/law.html