I tend to largely agree with Jonathan Adler's post on this; but I thought that I'd add some data, for whatever it's worth (I realize that different people have different views of how relevant or dispositive such data is):
1. A 2002 Sports Illustrated survey reports:
Asked if they were offended by the name Redskins, 75% of Native American respondents in SI's poll said they were not, and even on reservations, where Native American culture and influence are perhaps felt most intensely, 62% said they weren't offended. Overall, 69% of Native American respondents--and 57% of those living on reservations--feel it's O.K. for the Washington Redskins to continue using the name. "I like the name Redskins," says Mark Timentwa, 50, a member of the Colville Confederated Tribes in Washington State who lives on the tribes' reservation. "A few elders find it offensive, but my mother loves the Redskins."
2. The Annenberg Public Policy Center National Annenberg Election Survey 2004 (conducted in 2003-04), reports:
Most American Indians say that calling Washington's professional football team the "Redskins" does not bother them, the University of Pennsylvania's National Annenberg Election Survey shows.
Ninety percent of Indians took that position, while 9 percent said they found the name "offensive." One percent had no answer. The margin of sampling error for those findings was plus or minus two percentage points.
Because they make up a very small proportion of the total population, the responses of 768 people who said they were Indians or Native Americans were collected over a very long period of polling, from October 7, 2003 through September 20, 2004. They included Indians from every state except Alaska and Hawaii, where the Annenberg survey does not interview. The question that was put to them was "The professional football team in Washington calls itself the Washington Redskins. As a Native American, do you find that name offensive or doesn't it bother you?"
3. There are obvious problems with polling American Indians -- the difficulty of getting reliable data from such a small group (which the Annenberg pollsters solved by asking a vast number of people, and which the Sports Illustrated pollsters solved by oversampling in census tracts which have a high fraction of American Indians, and then weighing the responses accordingly), the uncertainties about who really is an American Indian, the danger of undersampling Indians who are too poor to have telephones or alienated enough from white culture that they want little to do with pollsters, and so on. Nonetheless, while this may not be perfect data, it's the best data that I've seen, and it's certainly better than people's perceptions of what Indians think, which are of course prone to much more serious problems of representativeness (since such perceptions may be heavily skewed by one's own preconceptions, by one's circle of friends, or by the tendency to hear more from activists -- in any group -- than from rank and file members).
4. Finally, while I'd have thought that most Indians would indeed be offended by the term "Redskins," given that it has often been used as a pejorative, the results that the surveys report are not at all implausible: Given that naming a team after some person or group is usually a sign of respect -- one would rarely name a team after something that one thinks is weak or contemptible (the U.C. Santa Cruz Banana Slugs are a rare and facetious exception) -- it seems quite reasonable that many Indians would focus on that more than they would on disrespectful uses of the same term in other contexts.