The Democratic party is not ideologically humongous, and I think there is quite a few people that fits the definition of centrist to a T.I'd still argue the party on the by leans left then. Even with the albatross of the senate/EC. The party pushes for leftwing social issues and tries to go for leftwing economic ideas.
Slow progress is progress to me. I mean, we've got AOC and more SocDem/DemSocs now.
Picking the definition from wiki: a political outlook or specific position that involves acceptance or support of a balance of a degree of social equality and a degree of social hierarchy, while opposing political changes which would result in a significant shift of society strongly to either the left or the right.
I also think that when you look at the policy outcomes of the Obama administration, it's very hard for me to call them left wing, but we might working with different definition of the term left and right here.