They exist, but are only really relevant at the local level, or rarely as a spoiler effect if one gets vaguely popular. This isn't so much that people don't want other options, but mostly because the US system is badly designed. The US has a first past the post, winner take all type system, ie, if you win the most votes in a given election, you win that spot and it's all yours. That makes some intuitive sense, but is actually not the most democratic option, as it means that parties that have, say, 20% of the population supporting them don't get 20% of the seats, they get none of them, because for each individual seat, they won't win the most votes. Worse, such a party will cause the major party it is less similar to to win, because it's voters voted for them rather than the major party it was most similar to, so even if the voters on that side of the political spectrum are in the majority, their votes are split among multiple parties where their rivals that stay as one party can then be the single largest one. The US system accidentally makes it mathematically inevitable for two and only two parties to dominate.

Historically they have switched up once or twice, when one party became so unpopular that it basically became nonviable, and a different party rose to replace it, and once the current major parties have swapped ideology more or less, but this kind of thing is very rare.