In the last 70 years 99.34% of Senate seats and 99.92% of House seats have been held by Democrats and Republicans, with the remaining fraction being independents and people who were originally elected under one of those two parties. For presidents you have to go back to before the civil war to find someone who isn't from one of the two modern parties. Obviously not the whole story (local / state), but that seems pretty compelling to me.

Disclaimer This will be primarily about presidential elections because I do not feel qualified to discuss all of the history of the congressional elections.

The short answer is no. There have generally been two dominant parties although there are almost always multiple other parties that exist at least in name, though they often lack electoral success. Starting after the creation of the Constitution, there were the democratic-republicans and the federalists. Then the Whigs and Democrats were the major contenders. Finally, upon reaching the civil war, we get the current two parties. You can see a list of election results here.

There have been times where more than two parties had some electoral success, but they have generally been limited. The Republicans and Whigs coexisted with the Democrats for a while, but it was less than ten years. Then the Whig Party fell apart. The "dixiecrats" existed along with the Democrats and Republicans for only the 1948 election and were splinter group of Democrats rather than completely new party regardless.

The reason for this is because of the elements of the first past the post system that are explained here. Essentially the system makes it beneficial for people to vote for one of two major parties.

tl;dr There are always more than two parties that exist but rarely more than two that are major contenders in the presidential election.

There has been significant influence from a third party. The Populists in the 1890s were taken over by the Democratic Party.