Unfortunately, the reaction of Americans to various goings-on in Europe is beyond my wheelhouse, so I can't provide a direct answer to the main question. That being said, I've written a previous response that detailed the history of the American Medical Association's opposition to Medicare and Medicaid in the United States, which you can find here. It touches briefly on the general disapproval of socialized healthcare by the American populace and members of Congress, as well as some of the factors that wore down the hesitation sufficiently to pass Medicare and Medicaid in 1965.

In short, American citizens were on average less than enthused by the idea of universal healthcare in the first half of the 20th century. Similarly, there was actually significant opposition to Medicare and other socialized or universal healthcare concepts among professional groups and government officials. Concerns included aversion to federal involvement in social welfare, physicians wishing to remain independent from non-medical governing bodies, and allegedly socialist policies.^1 In response, proponents of socialized healthcare began by targeting the elderly - a choice voting bloc - which would ultimately result in the proposal of Medicare. The general public begins to warm up to the concept by the time of President Kennedy, who includes Medicare as part of his platform. Still, he finds it impossible to push through Congress before he is assassinated. Enter President Lyndon Johnson, who is elected with one of the largest vote shares in US history off a platform of championing JFK's policy measures. Only then does Medicare see the light of day.^2

1. DOI: 10.1377/hblog20150910.050461
2. DOI: 10.1016/j.jacr.2006.09.010