The Supreme Court
Which I suppose is why a group of American oligarchs, featuring some familiar figures like the Koch brothers and the Mercer family have poured millions into the so-called Federalist Society, an institution dedicated to getting its choices onto the Supreme Court. To that end they have promoted partisan figures like the current conservative bloc on the Court by systematically recruiting them early in their careers and greasing the skids to get them appointed.
The exceptional success of this project has now produced a US judicial system far more conservative than the American public on a wide range of issues. Not for the first time in US history, this means the Court has the ability to obstruct progressive or otherwise oligarch unfriendly laws for what will likely be decades.
There are, however, some measures a more liberal Congress and President could take. The constitution does not restrict the number of Justices on the Court, and from time to time that has been changed, though that (so-called court packing) seems like an ugly way to run a justice system. Another idea that I like is that Justices serve 18 year terms, with each President getting to appoint two during each term he serves. Obviously this would not prevent appointments from being partisan, but at least it should prevent stunts like that pulled by McConnell and the Senate Republicans during Obama's last term.
Paul Starr discusses some Court reform ideas and links to further discussion here.