This is rather a comment to the question than an answer (there is an answer already, and I could answer only for Germany, not for the US).
However, for Germany the claims are not unknown, either, and the asked numbers for 2011 are:
* I'm not sure what the total refers to, possibly it is the total of all federal taxes.
Source: German federal tax office data collection, table 2.2
Table 2.3 says that this covers the ca. 37 million tax payers (46% of inhabitans) another 27 million adults have 0 income tax (33 % of inhabitants). 17 million children (21% of inhabitants) are not considered for income tax.
So for political judgment, the numbers from the copied table should maybe be corrected by including the percentage of adults who are taxed at 0 €. (There are other detailed tables that make clear that the copied table refers to people actually paying taxes only)
Even among those who consider themselves upper or upper-middle class, fully 52% say upper-income people pay too little. Only 10% of this group says upper-class adults say people pay too much in taxes.
Maybe that is less astonishing if read together with the table to Q 5 (asking the class) in the details of the survey: The "upper class" is composed of 90% who see themselves as upper middle class, and 10% who see themselves as upper class. Meaning that 90% of those counted as upper class do not consider themselves upper class.
I've seen numbers for Germany that suggest that there is a substantial gap between who is considered rich by "normal people" and who is considered rich by definition (political discussion). Here a politology prof says in an interview that his students (keep in mind that German universities have no tuition fees comparable to the US) name about 15000 €/month net as threshold for "income-rich", whereas the official wealth-and-poverty report uses a threshold of 3250 €/month net wage (rough estimate: 7500 €/month gross). So there is a gap of a factor of 4.5. That is comparably extreme, but this statistics shows the same trend (the lowest category in the diagram corresponds to the median income over the tax payers, i.e. people that contribute ca. 6 % of the total income tax volume (Wikipedia, Tax payer's federation). Both sources also say that a similar effect happens for low incomes: they do not perceive themselves as as low income percentile as they actually are. Seems to be same in Argentinia as well, where people from the lower decile perceive themselves as belonging to the 4th decile, while those from the 10th decile perceive themselves in the 6th.
Also this finding is IMHO less astonishing if read together with the income distribution (at least for Germany): if there are many people with income close to the median (or any other percentile of interest), a comparably low absolute difference makes a high difference in rank (percentile). Therefore, also a low absolute error in estimating other people's income (e.g. the median) will make a higher error in placing yourself into the correct category. Of course there may be also a bias due to wishful thinking: in societies where equality is considered good, you'd like yourself to be close to the normal person.