Narrated by Harris, the video argued in favor of equity, or ensuring people reach the same results, over equality of opportunity.
"Equality suggests, 'oh, everyone should get the same amount,'" Harris said.
"The problem with that -- not everybody's starting out from the same place ... It's about giving people the resources and support they need so that everyone can be on equal footing, and then compete on equal footing. Equitable treatment means we all end up at the same place," she added.
In response to Harris' tweet, Cheney said: "Sounds just like Karl Marx." She was referring to the 19th Century philosopher who wrote the "Communist Manifesto."
"A century of history has shown where that path leads," she added. "We all embrace equal opportunity, but government-enforced equality of outcomes is Marxism."
Harris did not immediately respond via Twitter, but her campaign has distanced itself from the socialist.
“I look like a socialist?” former Vice President Joe Biden told a town hall last month. “I’m the guy that ran against the socialist, remember? I got in trouble through the whole campaign, 20-some candidates — ‘Joe Biden was too centrist, too moderate, too straightforward.’ That was Joe Biden.”