Rahm Emanuel was Obama's chief of staff. Hillary Clinton was his Secretary of State. His Vice President was Biden himself. His Secretary or the Treasury's resume is classic neoliberal.
Like, I can't even fathom how you would call this unhinged. Obama was firmly in the centrist/neoliberal wing of the party. He ran on hope and change, but he filled his cabinet with Clinton alums and Wall Street bankers. He ran under the banner of a progressive, but he governed under the same centrist banner as Clinton and Biden.
Did you forget how he wasted months of precious Congressional time by desperately trying to make the PPACA bipartisan? He let Republicans slow things down for months. He let them put all sorts of amendments into it. In the end, they all voted against it.
If Obama was famous for anything, it was surrendering in advance. This was a massive topic of discussion at the time. Obama was infamous for performative bipartisanship. He wouldn't propose a democratic version of a bill. He would start by magnanimously offering a compromise between the Republican and Democratic positions, hoping in vain to bring Republicans onboard. Republicans took his compromise-in-advance as weakness and never returned the favor.
Have you really forgotten history that quickly? Obama was a neoliberal to his core. It was his cabinet that negotiated the bailouts of the banks. Progressives at the time were arguing that any bailouts should be made contingent on keeping people in their homes, perhaps writing down the balances of underwater mortgages. Instead, the centrists in the Obama administration bailed out the banks and left working families to lose their homes.
Obama was firmly part of the neoliberal wing of the party, the same faction that's been ascendant since Clinton. So yes, it is literally the Obama wing of the party that progressives need to fight against. Remember, Obama wore the skin of a progressive, but he actually governed as a centrist.