Surveys are heavily influenced by the way you are asking questions.
"Should the NSA be able to snoop all of our email/phone/etc records, and store them for later?" --> NO
"Should the government be able to expand its limited search capabilities so that it can better prevent terrorist attacks?" --> WELL SURE
That was a terrible example of a second way of phrasing it, but I am certain there is a way to frame what they are doing in a way which leaves out the "collect all your things" nuance (;)) and therefore will sound reasonable to many people.
In the general case you will find that answers tend to trend in this way:
NO: "Should the gov't ${trample_our_freedoms}?"
YES: "Should the gov't ${catch_more_terrorists}|${protect_more_children}?"