There are different strains of the left in America. The two main ones are what I call the left or hard left and the Bernie wing. These two groups do not get along, especially after Hillary and the DNC stabbed them in the back in the run-up to 2016. Obama is part of the left or hard left. They were the ones who turned away from the working class and focused on victim groups to secure the votes for a win. And ended up losing over 1000 elected positions at the local, state, and federal level. So far as political power goes, they have it on the left.
The Bernie wing advocates for more socialist programs in our government. They want the us to be a serious social democratic society. I don't think that anyone is advocating for a pure socialist government, not even the Socialist Party of the US.
See platform here. While the Socialist Party does call for the social ownership of productive resources, they are not calling for government (or social) ownership of all property (land and buildings). So even they have abandoned pure socialism. In my last tour in Iraq I was pure socialism. In Iraq all property was titled to the government (it made me wonder why they needed to keep title information if they all said the same thing with regards to ownership). It caused us a lot of problems with the locals as they tried to return to what they said was their homes. I am sure many were trying to claim up (a better home), but we had no way to know because nobody owned their land and homes under Saddam. I don't know whether we found documents that showed who rented the land / home. Such documents were not found when I was there. Perhaps the locals hid them from us- there were more homes available than people due to deaths and migration, and I expect most wanted to claim up.
Currently the Bernie wing has little power, but that is changing. Younger generations of the left are drifting away from the hard left towards the Bernie wing. They will find out overtime that the Bernie platform is prohibitively inexpensive.
I use the term hard left above to lament the purging of the Blue Dogs from the Democratic Party. They were reasonable people and had some good ideas.