The idea that Barack Obama wasn't born in the United States has shown a lot of staying power, but few surveys have asked about it. One of those is a July 2010 poll sponsored by 60 Minutes and Vanity Fair magazine. In this survey, 25% said that they thought Obama was born in another country and 14% said they didn't know. The challenge in interpreting these results is to separate “pure ignorance” from “politicized ignorance.”
By “pure ignorance,” I mean people who don't know that the constitution limits the presidency to “natural-born citizens.” Such people might be neutral or even favorable about Obama being born outside the United States—they might even think it shows that America is a land of opportunity. The survey doesn't ask who you voted for in the last election, but we can look at groups that are heavily favorable to Obama: blacks, liberals, and people who approved of the administration's handling of the BP oil spill (only about 35% did at the time):
Not born in US Don't Know
Liberals 11% 6%
Blacks 12% 11%
Approve handling oil spill 11% 8%
The combined total of people who think Obama was born outside the United States and those who don't know is about 20% in all of these groups. So it seems that about half of the original total represents what I call “pure ignorance.” On the other hand, that suggests that about 20% of Americans are “birthers” to some degree.