Amy Zegart of Stanford’s Hoover Institute reports findings from a poll she conducted.

I originally thought that more knowledge would lead to higher levels of NSA support. That’s what NSA officials think, too. NSA Director Gen. Keith Alexander, in a speech in September, argued that surveillance programs have been sensationalized by the media: “And so what’s hyped up in a lot of the reporting is that we’re listening to your phone calls. We’re reading your emails. That’s just not true.” The implication is that Americans would be more supportive if reporting had been more accurate.
But my poll numbers suggest otherwise. … Among those who could correctly identify the DNI [Director of National Intelligence], 53 percent had an unfavorable view of NSA, compared to 33 percent for those who could not identify the DNI. Among those who said (correctly) that the NSA does not capture or kill terrorists, 64 percent had an unfavorable view of NSA, compared to 35 percent for those answered this question incorrectly. Among those who correctly responded that NSA does not interrogate detainees, 60 percent had unfavorable views of NSA, compared to 42 percent for those who answered this question incorrectly.

As Zegart suggests, this doesn’t mean that knowing more about the NSA makes people less likely to support it. It’s also plausible that people who are already inclined to dislike the NSA are motivated to look for more information about it. Or, put differently, with this kind of data, there’s no way to know if increased knowledge is causing people to like the NSA less, or if dislike for the NSA is causing people to find out more about it. It’s also possible that both increased knowledge and dislike are being driven by some other factor not included in the analysis. Still, it certainly isn’t good news for the NSA if those who are sufficiently interested to know something about it are more inclined to dislike it than not, as well as being more likely to dislike it than their less knowledgeable fellow citizens.