Our top court did the opposite -
https://en.wikipedia.org/wiki/Citizens_United_v._FEC
It would take an act of congress at this point. You usually hear whatever party with less representation complain about it, but once they get enough of their party in power in congress, they suddenly forget to do anything about it. It is one of the most noticeable aspects of corruption in the US.
At this point, the people would have to make a strong stand against this kind of corruption. But, to be honest, far too many people get sucked into wedge issues to think about anything productive regarding politics.
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While union donations are a bit understated and corporate donations are a bit overstated, they aren't off enough to make up the massive gap in union vs corporate donations...and that graph doesn't (obviously) include dark money that is almost exclusively corporate.
https://www.opensecrets.org/overview/blio.php
Business contributions (2013-2014) - 1.675 Billion
Labor contributions (2013-2014) - 140 Million