Politics in the US is not limited to the two parties. The population of the US has a wide range of political opinions that don't neatly aligned to the mainline Democratic or Republican views. Especially in the US, with its system of primaries, the real politics of the population are relevant even when the official election essentially only offers 2 candidates.
And in the real US, the Democratic party is to the right of a vast majority of its own voters' views, on issues such as Medicare for All most prominently, but others as well. It's even to the right of the views of large swaths of Republican voters on many issues, such as withdrawing from Iraq and Afghanistan. The Democratic party is much closer to the Center of the political opinions of the US population, at least on economic and foreign policy matters (I would say it's well in the center-right of American political views actually on those matters). It may well be on the 'real left' on social and family matters, to be fair.
Not to mention, there are many other political forces and voices, which form a clear left pole far to the left of the Democratic party (I gave specific examples), and they have large amounts of increasingly organized support. They will likely pull the Democratic party to the left instead of establishing a pure leftist party, but that is far from having happened. You can look instead at how much the extreme right has been pulling the Republican party right to see the mechanisms
So the way I see it, the US population has left leaning people, right leaning people, and centrists. Looking at the relative opinions of the population, the Democratic party is overall in the Center, and the Republicans are well on the right (these are overall generalizations). Of course, in the absence of better choices, leftist voters will generally vote Democratic, as the Center is preferable to them than the Right.
More importantly for this claim, papers like the NYT and networks like CNN are explicitly cultivating centrist beliefs (especially on economic and foreign policy matters), often leaning far more to the right on such issues compared to the majority of the population (look at Brian Williams repulsive praise of the 'beauty of our weapons' on MSNBC[0] as they were reporting on a US missile attack on a Syrian base).
[0] https://m.youtube.com/watch?v=jNHOJwgZyfo