The following is a rush transcript of the September 19, 2010, edition of "Fox News Sunday With Chris Wallace." This copy may not be in its final form and may be updated.

CHRIS WALLACE, ANCHOR: This is not the program we were planning to bring you. Christine O'Donnell, the surprise winner of the Republican Senate primary in Delaware, agreed to come here live in Washington today to take our questions.

However, late Friday night her campaign canceled, saying O'Donnell was exhausted and had to return to Delaware. Saturday morning O'Donnell called me and said this, "I got triple-booked. I had been invited to go to church and then a picnic. I have to keep my priorities to Delaware voters."

So we begin today with someone who has been critical of O'Donnell, master Republican strategist Karl Rove.

Karl, you've come under a lot of fire from conservatives this week for criticizing Christine O'Donnell. Let's watch.

(BEGIN VIDEO CLIP)

SENATORIAL CANDIDATE CHRISTINE O'DONNELL: Everything that he's saying is unfactual. And it's a shame because he is the same so- called political guru that predicted I wasn't going to win. And we won and we won big.

(END VIDEO CLIP)

(BEGIN VIDEO CLIP)

RUSH LIMBAUGH: If he had just gotten this mad at Democrats during the Bush administration, why, who knows how things would be different today?

(END VIDEO CLIP)

WALLACE: Add to that everyone from Sarah Palin to Michelle Malkin, Karl, and the argument seems to be you're part of the Republican establishment and you feel threatened by the tea party.

KARL ROVE, REPUBLICAN STRATEGIST: Well, this is actually about what is a winning strategy. There are serious questions that have been raised about Miss O'Donnell's background, character, statements and previous actions.

You can either say, "We're going to ignore those questions and plan on people's dissatisfaction with Barack Obama and his policies, with all the spending, deficits and debt and the Obama health care plan, and just ignore the personal questions and count on people's animosity towards those -- towards those Obama actions in order to win the election."

Or you can take the perspective that I do, which is people are not going to hear these arguments about President Obama and his policies and what the Democrats are doing in Washington as long as these questions are out there.

And frankly, here's the data. If you take a look at primaries like those in Nevada, Kentucky, Colorado, Missouri, Florida, where a Republican, strong conservative, won the primary, they immediately jumped to the lead in the polls.

In Nevada, Sharron Angle went 11 points ahead of Harry Reid immediately after she won the primary.

In Kentucky, Rand Paul moved 25 points ahead.

In Alaska, Joe Miller moved eight points ahead.

In Delaware, the Rasmussen poll says Christine O'Donnell remains 11 points behind Chris Coons, the Democrat, after this primary.

So look, we all want to have a -- I want to have a Republican Senate. I assume all the rest of these people want to have a Republican Senate. The question is what's the best strategy to get there. And if you take the strategy, "I'm going to ignore these questions," fine. Go ahead and pursue that strategy.

I, frankly, think a winning strategy requires coming to grips with these questions and explaining them in the most sympathetic way possible so that people unblock their ears in Delaware and begin hearing the broader message.

WALLACE: Well, you talk about explaining them in the most sympathetic way possible. Now Christine O'Donnell has canceled on us and another Sunday show, her campaign citing exhaustion. She says it was overbooking.

And now, as you probably know, there's a tape floating around of her back in 1999 saying that she dabbled in witchcraft. I mean, that's not going to help either of those, is it?

ROVE: Well, look, if you say that things like not paying your federal income tax and getting slapped with a lien is unfactual, you're obviously taking the perspective of "I'm going to ignore these." And again, that's a legitimate campaign strategy. It depends upon getting a -- you know, depending on this wave of animosity towards President Obama in order to get elected.

I, frankly, think she made a smart decision by not getting on the Sunday shows this week. She shouldn't have accepted in the first place. But you know, she needs to talk to the people of Delaware. It's Delaware voters. It's not conservatives around the country who are going to determine her -- the outcome of this election. It's going to be Delaware voters who determine it. And there is, as I say, resistance.

When this woman wins a stunning upset -- and incidentally, I didn't predict she wouldn't win, but she won a stunning upset. And this is the moment when she should be grabbing the imagination of the people of Delaware and moving ahead in the polls like these other candidates did around the country.

I mean, Roy Blount has now got a 10-point lead building upon the momentum that he got from winning the Republican primary in Missouri.

In Ohio, Rob Portman now has a 20-point lead after trailing before the Republican primary his Democrat opponent.

WALLACE: I want to move on to other things, but I just want to ask you quickly, this new tape in which she said on the TV show "Politically Incorrect" in 1999 that she dabbled in witchcraft -- how damaging is that?

ROVE: Well, you know, in southern Delaware, where there are a lot of church-going people, they're probably going to want to know what was that all about. And again, she said it on television when she went on the -- on the Bill Maher show.

And I -- 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."

I don't think the people of Delaware have or are accepting that as a reasonable explanation. And until they do, they're going to be resistant to hearing the bigger, broader, more important message.

WALLACE: OK. I want to ask you about the other big political development this weekend, and that is the fact that in Alaska, Senator Lisa Murkowski, the incumbent Republican who lost to Joe Miller, who's going to be our next guest, the tea party favorite in the Republican primary, has now announced she's going to run as a write-in candidate.

Couple of questions. One, can she win? Or two, can she siphon enough votes away from Miller that the Democrat in the race, Scott McAdams, will win?

ROVE: Well, the answer to the first one is absolutely no, she can't win. Under the law, you have to carefully spell the name exactly correct. Everybody, go to your pencil and paper and write down the name "Murkowski" and see if you got it right. No, she's going to lose. Now, the bigger, more important question is is she going to keep a Republican from winning. 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.

This is sad and sorry. She should not be doing this. My hope is that the Republicans and conservatives in Alaska recognize the bigger issue, which is defeating President Obama's agenda and go for this highly qualified Republican nominee, a West Point graduate, a military veteran, a graduate of one of the nation's most prestigious law schools, a former magistrate judge, a practicing attorney in the state and an active Republican.

He won it fair and square, and Lisa Murkowski should not pursue this very, very sad line that she is pursuing.

WALLACE: Karl, let's step back and take a look at the bigger picture. In at least seven states that we count, the tea party insurgent beat the establishment Republican candidate in Senate contests. What's happening in the GOP? Is it a civil war? Is it a battle for the soul of the party? What's going on?