"She doesn't know anything," Wasserman Schultz said on CBS' Face The Nation, responding to a charge by a fellow guest, former Mass. Gov. Jane Swift, that Palin has been forced to undergo scrutiny in the media that some would characterize as sexist.
"There shouldn't be a double standard," Swift said. "We shouldn't ask of her questions about her ability to do the job that we wouldn't ask a guy in a similar circumstance.
"But I think that we also have to acknowledge that, because we've had so few women running for these high-level offices, although this is a great year on that front, that we're also not attuned to hearing women's voices and to seeing them in these positions.
"So it may be that we have to be most attuned to not having a double standard, to not asking any female candidate of either party to clear a bar that we wouldn't ask a male candidate in the same situation to clear."
Wasserman Schultz disagreed that Palin has had to meet an unfair standard.
"All Sarah Palin is being asked to respond to is whether she's up to the task," she said. "And it is absolutely fair game. And all I've seen is her being asked about her background, her experience, what qualifies her to be vice president, and whether she knows anything.
"So the tough questions that have been asked of Sarah Palin thus far just have been about the fact that she doesn't know anything and isn't ready to be vice president. That's fair game and it has nothing to do with her gender.
"You're saying she doesn't know anything, or you're saying that's what she's been asked about?" asked host Bob Schieffer.
"Well, she's been asked what she knows," Wasserman Schultz said. "She's been asked to demonstrate her foreign policy knowledge, which she clearly has very little, based on the Charlie Gibson interview. I mean, she didn't know what the Bush doctrine was. She really had almost no grasp of America's foreign policy. She really knew very little about domestic policy.
"Quite honestly, the interview that I saw and that Americans saw on Thursday and Friday were similar to when I didn't read a book in high school and had to read the Cliff Notes and phone in my report. She's 'Cliff-Noted' her performance so far. And all of that is fair game. The American people deserve better than that."
"I think what we're looking for and what the McCain-Palin ticket is talking about is changing the way Washington works. And she does have experience in that for sure.
"She has shaken up Alaska politics. And she has an instinct about reform and ethics that's very, very strong that people in this country are looking for.
"So I think to say that, well, she has very low depth of foreign policy experience - name one governor who has become president who has had in-depth foreign policy experience.
"The fact of the matter is, John McCain has vast foreign policy experience, and he's the candidate for president," said Hutchison.
"He chose Sarah Palin because she's going to support those views," Napolitano said. "And that's why she shouldn't be the vice president."
Read the full "Face the Nation" transcript here.
By CBSNews.com producer David Morgan.