Cheney, who served eight years as George W. Bush's vice president, made his remarks during an interview
with ABC News on Sunday.
"I like Governor Palin. I've met her. I know her," Cheney told ABC's Jonathan Karl. "But based on her background... I don't think she passed that test... of being ready to take over. And I think that was a mistake."
Appearing on Fox New's "On the Record" Tuesday, Palin responded
to Cheney's assertion with wry sarcasm.
"Well, seeing as how Dick-- excuse me, Vice President Cheney-- never misfires," she told host Greta Van Susteren, a reference to the 2006 incident in which the former veep accidentally shot
a friend in the face while quail hunting in Texas, "then evidently he's quite convinced that what he had evidently read about me by the lamestream media, having been written, what I believe is a false narrative over the last four years, evidently Dick Cheney believed that stuff and that's a shame."
Palin then opined that the "real mistake" would have been if she had "not answered the call" to run for vice president.
"Everybody misfires once in a while," she said before offering this assessment of the Republican establishment:
"In the GOP establishment, you know what I've found, Greta? Sometimes you're the Louisville Slugger, sometimes you're the ball. And evidently in these last months-- per many, many comments from those within the GOP establishment-- I'm the ball."