Ms Cheney, daughter of former president Dick Cheney, on Monday shared a video of Ms Ocasio-Cortez in which she claimed the Democratic party used to be so popular politicians in the 1940s had to amend the Constitution in order to stop Franklin D Roosevelt being re-elected.
The comment was mocked by critics who pointed out Roosevelt died two years before Congress ratified the 22 Amendment, which prevented presidents from serving more than two terms.
“We knew the Democrats let dead people vote. According to @AOC, they can run for President, too,” Ms Cheney tweeted in reference to a conspiracy theory espoused by Donald Trump.
“I see from your dead people comment that you get your news from Facebook memes,” responded Ms Ocasio-Cortez, who linked to a Newsweek article she said would “clarify your misunderstanding” of the 22nd Amendment.
Despite the crticism, Ms Ocasio-Cortez was at least partially justified in her claim Roosevelt's popularity forced a constitutional change.
Lawmakers were already pushing for the 22nd Amendment when Roosevelt won an unprecedented fourth term in 1944.
He died less than three months after his inauguration the following year, before a Republican-controlled Congress ratified the amendment in 1947.