Is that true? One's options are limited if all one can do is vote for representatives, instead of directly voting on an issue themselves.

It's helpful to distinguish between the side-effects coming from one's vote and the intention/motivation for that vote. (This is called the doctrine of double effect.)

I would be surprised if many poor people vote with the intention of giving tax cuts for rich people, instead of voting for a candidate who they feel resonates them for other reasons, where it is an incidental fact that this candidate will push tax cuts for rich people.

This is true and I was being a bit snarky, but let us not forget the story of "Joe the plumber"