Left-leaning and major? No. Considering the countries that the US is compared to, there's not really a centre-leading major news source, either.
CNN is pretty far left and kind of major.
Wow ... CNN is definitively not left-leaning. It fully buys into the capitalist ideal. It's more like neoliberal. That's not what I had in mind when I said "left".
You only think this because the Overton window has shifted so far to the right that the center right CNN appears far left because of how far right the ruling party is.