In 1947, a Gallup Poll asked "if a man makes one million dollars a year, how much of it do you think he has to pay in taxes?" In 1998, another Gallup survey asked "if a person makes one million dollars a year, how much of it do you think that person has to pay in taxes?" The comparison:
less than 20% 10% 38%
20-29.9% 12% 20%
30-39.9% 6% 16%
40 and over 58% 10%
DK 14% 16%
Since 2010, there have been a couple of surveys about how much people with high incomes should pay. One was "What maximum percentage do you think...individuals and families with incomes between two hundred and fifty thousand and a million dollars should pay each year in income taxes?" The median was 21-25%. Another asked "About what percentage of income should someone making a million dollars a year pay in taxes--including federal, state and local taxes?" The median for that was 26-30%.
A 2012 CNN/ORC survey showed support for higher tax rates: "Would you favor or oppose a proposal to change the federal income tax rates so that people who make more than one million dollars a year will pay at least 30 percent of their income in taxes?" found 72% in favor and a Gallup Poll found 60% in favor for a similar question.
I believe that people in the top income category currently pay a bit more than 30% on the average (according to the IRS). That is, they pay more than what most people think they do. I don't know if there's an estimate for 1947--I don't have time to check now, but I'll try to find something later. I expect that it was higher today, because taxes on top incomes had been raised during the Second World War.
PS: With inflation, a million dollars in 1947 was worth about 16 million in 1998. So it's possible that explains some of the differences--that people believe that rates are steeply progressive beyond some point--although I doubt it. I think at both times most people reacted to a million a year as just meaning "rich."
[Data from the Roper Center for Public Opinion Research]