It's often suggested that Americans care more about equal opportunity than people in other nations (see the quotation from Luigi Zingales in my recent post). You can support this with examples from history--the United States was traditionally a leader in providing public education, although other countries have caught up with us recently, and it still has less educational tracking than most other nations.
What about surveys? The 2009 ISSP survey discussed in my last post has one question that directly involves "a level playing field"--whether it's just that rich people can buy a better education for their children. The other questions, except maybe the one on medical care, are about equal results--helping the poor and unemployed or taking from the rich. Americans rank 31st among 38 nations on the education question, compared with an average of 32nd on the others (high numbers represent less egalitarian sentiments). However, there are some nations in which rankings on the education question are substantially different from rankings on the others.
More likely to see it as unjust
For example, Sweden is 12th most egalitarian on education, an average of 22nd on the others. With the Scandinavian countries, this is probably because some of the questions involve implicit comparisons to the present; since the government already does a lot to equalize conditions in those countries, people are less likely to be in favor of doing more. I don't know enough about Belgium or Cyprus to offer a guess about why they are on the list.
Less likely to see it as unjust
All of the East Asian nations in the survey show up on this list. For example, people in South Korea are fairly egalitarian overall (an average of 12th on the other questions), but don't have a problem with rich people buying better education for their children (32nd).
In any case, Americans don't seem to make much distinction between equal opportunity and equal results--by international standards, we (and Anglo-Saxon settler societies more generally) don't care much about either one.