They're saying two very different things.
In the standoff over access to the San Bernardino shooter's iPhone, who's right: Apple or the FBI?
A variety of opinion polls of varying rigor have been conducted in the week since Apple (aapl) was ordered to help the FBI attack the iPhone's PIN code. The survey that was getting the most press attention Tuesday, from the well-regarded Pew Research Center, showed 51% of Americans supporting the FBI, 38% supporting Apple, and 11% not knowing enough about the dispute to form an opinion. [See UPDATE below.]
That's not what the Internet polls are saying. They strongly favor Apple.
For comparison purposes, here are all the survey results I've seen, redrawn and color-coded (blue for Apple, red for the FBI):
Not all polls are created equal, of course. Pew is using peer-reviewed methodology to get a representative sampling of the American electorate. The Internet surveys, by contrast, use no methodology whatsoever. Since anybody on the Internet can vote (as often as they want, in some polls), respondents predisposed to favor Internet security are over-represented.
Yet even Pew acknowledges that no poll is perfect. "In addition to sampling error," it warns, "one should bear in mind that question wording and practical difficulties in conducting surveys can introduce error or bias into the findings of opinion polls."
The national debate about the role of strong encryption in a free society is in its early days, and public opinion is likely to shift many times before the question is codified into law. To put the issues in a broader context, here's the latest Pew survey weighing fear of terrorism in the U.S. against concern for civil liberties.
Given where things stood in December, with 56% of Americans concerned that the government isn't doing enough to protect the country and only 28% worried that it has gone too far restricting civil liberties, support for the FBI (51%) in its standoff with Apple (38%) might be viewed as weaker than expected.
UPDATE: A Reuters/Ipsos poll of 1,108 Americans published Wednesday shows public opinion tilting Apple's way (46% to 35%), with Democrats showing more support for Tim Cook's position than Republicans. Americans also support, by a smaller margin, the government's right to look at data their smartphones in order to protect against terror threats. It's not clear if they can have it both ways.