Representatives do reflect the will of the people who elected them. The real problem is, on an individual level, your vote is statistically irrelevant, so it's easy to disassociate, and to blame "the others" who, collectively, have a vastly more powerful say over who represents you than you do. "They ought to vote more like how I want them to." you can say, "They don't vote correctly and I can't stop them, so it's the system's fault for giving them power over me!" This, of course, completely undermines the entire point of democracy, that it represents the collective will of the people, not any individual's arbitrary will.
A representative democracy works even if you don't believe it does. It stops working if everyone doesn't believe it does, which is certainly not even close to the case in the US.