The problem is technological, as deficiencies in relied-upon communication technologies is what have allowed surveillance to scale from human intelligence on prioritized targets to dragnet
scrutiny of everybody. No matter how much effort is required, "law enforcement" will always be snooping on
some suspects - what we'd like to prevent is an institutionalized fishing expedition.
You're signing up for a losing game. The myth of Democracy (tm) is another layer of control over individuals.
1. Most people will never have a problem with what the NSA is doing. They support the NSA's goals (tautology, since as you've mentioned, it is responsible to the majority), and if its methods end up causing harm to enough people, they will simply be adjusted to reduce aggregate harm (not to rule out any possible harm). The feedback loop of democracy works on specific actualities, not hypothetical corner cases.
2. The most memetically fit ideas are the simplest ones that elicit the strongest feelings (see: bikeshedding). Outrage peddlers swamp the political reception bandwidth with lowest common denominator controversy - usually judgments on other's lifestyles.
3. Even if there is a widespread preference to reduce the scope of the NSA, the people simply do not have the transmit bandwidth to make this preference clearly known. And they are easily led into squandering their input on the aforementioned manufactured controversy.
4. Elected figures don't actually run the government, the entrenched bureaucracy does at an imperceptible glacial pace. The elected figures run interference by making the majority believe they voted for this shit.