That's extremely simplistic. The complicated truth is:

1. It's a law of political science (Duverger's specifically) that a first-past-the-post system leads large, mass-appeal parties, and parties that don't go for mass appeal will fail.
2. In the US, the political balance is further pushed to the right by a) unequal representation that typically favors rural states and districts, most egregiously in the Senate, and b) denial of representation to particularly blue parts of the country like PR and DC. This means that relative to the country, Democrats cannot be as far left as Republicans are far right and still hold power. This can be observed in the simple fact that in the 21st century, Democrats have won 5/6 national popular votes, but have only controlled the Senate in 4/12 sessions.
3. From 1 and 2, it follows that Democrats would effectively lose what little political power they have by taking a firm leftist stance, leading to effectively a one-party far right state.