I'd argue that the apathy comes not from district size but from the fact that nobody even knows what their representative is up to. Public attention is entirely on the President. Nobody knows or cares about their own representative's actions.
Were there a way to make the public aware of what their own representative is voting and arguing, voter interest would pick up.
(And in any case, if someone "feels the power of their vote" in a smaller district, they'd also realize that with several thousand representatives, their representative is a lot less powerful.)