Here's the "law": https://en.wikipedia.org/wiki/Duverger%27s_law
So you might think it's possible. But it's a case of in theory, in theory and in practice are the same, in practice, they ain't.
And that is what FPTP is designed for. To over-reward those at the top of the leaderboard. It's designed to not be representative.
It's actually not that different in practice There are a large range on views in both parties, but you put on the Democratic or Republican label in order to build a majority coalition. This is sort of like how the Westminster parliamentary system works: labor forms a government with the greens. Labor has more seats by far is and is mostly in charge, but the greens get some government positions and a little influence on the agenda of state.
As a recent example of this here Bernie Sanders was not at all a Democratic party member but "joined" with them to try and get enough support.
Smaller parties... like the SNP? 7% of the seats from 4% of the vote. Seems to fly in the face of what everyone says about what is possible under FPTP. And what's more they've been effective in influencing what happens in parliament!