Since she won the GOP primary for U.S. Senate in Delaware, O'Donnell has been dogged by past statements, including the assertion that U.S. scientists have created mice with "fully functioning human brains" and her claim to have "dabbled in witchcraft" in the late 1990s.
"There are serious questions that have been raised about Miss O'Donnell's background, character, statements and previous actions," Rove said on Fox News Sunday.
"My view is she can't simply ignore it. She's got to deal with it and explain it and put it in its most sympathetic light and move on. But she can't simply say, 'Oh, these are unfactual and not true and just ignore them for the -- go to my Web site and ignore them.'"
O'Donnell canceled appearances on "Fox News Sunday" and CBS's "Face The Nation," citing scheduling conflicts and exhaustion.
Rove also said U.S. Sen. Lisa Murkowski of Alaska, who lost her GOP primary to Tea Party favorite Joe Miller, has no chance of winning the general election as a write-in candidate.
"Absolutely no, she can't win," Rove said, adding, "Who would have thought that one of the most conservative states in the country ran the risk of having two liberal Democrats who follow the Obama line representing it in the United States Senate? And that's what she could do as a spoilsport."