Voter apathy in the US to some extent mirrors the ineffectiveness of voting. In congressional elections in particular, only around a quarter of races are competitive, usually only being a rubber stamp until His Lordship the Incumbent retires/dies or the districts are reapportioned (at which point the election is settled by a primary with even more abysmal turnout). Your vote dies in your district, so any surplus of votes in favor of the winning candidate does zilch, just as any vote for the doomed party in that district does absolutely nothing. This means that nationally, most of the votes cast in congressional elections have no effect whatsoever.
Since the districts themselves are massive (~700,000 people was the average the last apportionment shot for, but some go over a million) there is effectively zero chance for a third party candidate to win any federal election. Congressional elections would be the "easiest" for a third party candidate to win, but campaigning effectively enough to win a plurality of votes in a district as large and chimerical as the congressional districts is nearly impossible.
Independents can still win, but almost always only by starting as a party incumbent and leaving it, and this is increasingly rare:
The electoral college is in some ways even worse, because in most states the entire state becomes a winner-takes-all district, leading to even more glaring inaccuracies and vote-wasting, but ultimately it's the congressional elections that have the most impact on the party structure as a whole.