On Friday’s CBS "Early Show," co-host Harry Smith interviewed Hillary Clinton and wondered if she would step aside for the good of the Democratic Party: "More important for you to be elected, or for a Democrat to be in the White House a year from now?"

Smith began the interview by asking Clinton: "And you stopped, you paused, you drew a breath, and you said you were honored to be there with Barack Obama. And I whispered, as you said that, 'valedictory.' Was that the beginning of the end of your campaign?" Smith went on to wonder if a long drawn-out nomination fight was "worth it"given Obama’s lead:

And I thought I saw some of the fight leave your body last night. I thought I saw there was almost a sign of body language like this guy has won ten states in a row. He has a significant lead in delegates. You know, is it worth going after every single vote tooth and nail for the next two, three, four weeks?

Even at this tough question, Clinton looked for sympathy: "And probably what you saw was, you know, lack of sleep, which finally does catch up to you with all of the cross-country traveling we're doing." On the issue of party unity, Clinton responded: "Well, we're going to have a unified party...And we're going to do everything we can to elect whoever our Democratic nominee is."

In a later segment with "Face the Nation" host Bob Schieffer, Smith again wondered if it was time for Clinton to step aside for Obama:

You're starting to hear these rumblings, though, of suggestions that maybe it's time that she step aside. Think about it, ten states in a row. You've got a significant lead in delegates. There's also the popular vote, which he has a pretty large lead on. There's an argument out there that maybe she should. Is there any chance...that she steps away before --

Here is the full transcript of both segments:

7:00AM TEASER:

HARRY SMITH: The Clinton-Obama debate. Sharp attacks ending on a scene-stealing note.

HILLARY CLINTON: I am honored to be here with Barack Obama. I am absolutely honored.

SMITH: This morning, Hillary Clinton live.

7:03AM SEGMENT:

HARRY SMITH: But leading our news today, Senator Hillary Clinton and her indefatigable fight to the finish. We're going to talk live to her in just a moment, but first CBS News Chief White House Correspondent Jim Axelrod with the highlights of last night's debate. He's in Austin, Texas. Good morning -- good morning, Jim.

JIM AXELROD: Well, good morning, Harry. With Barack Obama surging ten straight victories in state contests, Hillary Clinton needed a big moment last night, something to force a closer re-examination of her rival. She didn't get it. Much like their first face-to-face debate, Hillary Clinton came out cordial.

HILLARY CLINTON: Senator Obama and I have a lot in common.

AXELROD: And was met by an equally civil opponent.

BARACK OBAMA: And that's an area where Senator Clinton and I may have a slight difference, but I'm happy to let her speak first.

AXELROD: Clinton did throw some punches. For instance, on allegations that Obama copied his friend's lines in his speeches.

CLINTON: Lifting whole passages from someone else's speeches is not change you can believe in, it's change you can xerox.

AXELROD: But it fell flat. And Obama countered effectively.

OBAMA: This is where we start getting into silly season in politics, and I think people start getting discouraged about it.

AXELROD: There was back-and-forth over Cuba, healthcare, and immigration. But on a night when Hillary Clinton needed to force an error, contention and disagreement took a back seat to graciousness.

CLINTON: No matter what happens in this contest -- and I am honored -- I am honored to be here with Barack Obama. I am absolutely honored.

AXELROD: Perhaps most striking, Hillary Clinton says very directly, if Barack Obama is all speech, no substance, or all hat, no cattle, as they say here in Texas, it's been Hillary Clinton's central argument. She was asked about it directly. She ducked. Harry.

SMITH: Jim Axelrod live in Texas this morning, thank you very much. And joining us now is Senator Hillary Clinton. Good morning, Senator.

CLINTON: Good morning, Harry.

SMITH: I want to go back to that moment at the very end of the debate last night. You had answered a very emotional question about some of the things that you have seen during this campaign. And you stopped, you paused, you drew a breath, and you said you were honored to be there with Barack Obama. And I whispered, as you said that, 'valedictory.' Was that the beginning of the end of your campaign?

CLINTON: No, of course not. It is a recognition that both of us are on the brink of historic change. You know, I'm very proud that we have the two of us in this contest seeking the Democratic nomination, hoping to become our next president. Obviously, I believe that, you know, my record and my plans for what we can do for our country are ones that, you know, really are rooted in my experience and my strength, being able to bring about the positive differences that people talk to me about. You know, there are, you know, the kind of contrasts between us. You know, you saw that last night. I have a health care plan, like Senator Edwards did before, that would cover everyone and Senator Obama's doesn't. And I have a specific plan to stop home foreclosures, that if I'd been president, would have already been in effect.

SMITH: Let me -- let me --

CLINTON: So there is so much that I have been, you know, working on my entire life. And it's -- it is very motivating to me because I can see the differences that I've already made in helping people get health care in Texas and Ohio, and I'd like to continue that.

SMITH: Here's the thing. I'm watching this debate last night. And as you well know, we've been paying very close attention all the way through for so many months. And I thought I saw some of the fight leave your body last night. I thought I saw there was almost a sign of body language like this guy has won ten states in a row. He has a significant lead in delegates. You know, is it worth going after every single vote tooth and nail for the next two, three, four weeks?

CLINTON: Well, it certainly is, Harry. And probably what you saw was, you know, lack of sleep, which finally does catch up to you with all of the cross-country traveling we're doing. But, you know, I have a great campaign here in Texas, a great campaign in Ohio and the other states that are going to be coming up. And it's because people really believe that, you know, we are going to make a difference. That as president, I would be able, on day one, to begin turning the economy around, that I could step in and deal with the problems. We have an embassy on fire in Serbia, you know? We have potential changes in Pakistan and Cuba. We've got the independence of Kosovo. You know, problems come to the president at 3:00 in the morning. There are no predictions. And I think I am, you know, prepared and ready to handle those problems no matter what they are.

SMITH: Last question, very quickly in closing, more important for you to be elected, or for a Democrat to be in the White House a year from now?

CLINTON: Well, we're going to have a unified party. I've said that repeatedly. And we're going to do everything we can to elect whoever our Democratic nominee is. Obviously, I think by strength and experience and leadership and preparation, I would be the better president, or I wouldn't be up here at, you know, 5:00 or 6:00 in the morning talking about what I want to do and reminding people about the changes I've already brought about. You know, if you want to know what somebody will do, look at what they have done.

SMITH: Hillary Rodham Clinton, thank you very much for your time this morning. You can't say I didn't try. Thank you, Senator.

CLINTON: It's always good to talk to you, Harry.

SMITH: Take care.

7:17AM SEGMENT:

HARRY SMITH: The pressure sure was on Hillary Clinton during last night's debate. She lost ten primaries in a row to Barack Obama. She needs to stop his momentum. Did she succeed? Joining us is Bob Schieffer, CBS News Chief Washington Correspondent and host of "Face the Nation." Good morning, Bob.

BOB SCHIEFFER: Good morning, Harry.

SMITH: Was there a discernible winner or loser last night? What are your thoughts on the debate?

SCHIEFFER: I don't think so. I don't think there was any game-changing incident that took place. But I was just watching the interview that you conducted with her. I think what happened here last night is Hillary Clinton understands she's behind now. Clearly he has the momentum. Every poll suggests that. But beyond that, what she understands is that she has somehow got to go after him and draw a contrast with him, but do it without offending African-American voters. I think you saw that throughout the debate last night, especially at the end when she said, it is just a pleasure to be here with you. She knows this thing is tight, but she also understands, I think, that if she does wind up getting the nomination and she offends the African-American community in doing so, the nomination won't be worth anything because a Democrat, Harry, simply can't be elected without the support of African-Americans.

SMITH: Yeah. You're starting to hear these rumblings, though, of suggestions that maybe it's time that she step aside. Think about it, ten states in a row. You've got a significant lead in delegates. There's also the popular vote, which he has a pretty large lead on. There's an argument out there that maybe she should. Is there any chance in the 30 seconds or so I have left that she steps away before --

SCHIEFFER: I don't think so, Harry. I think she's been at it this far, she's certainly going to go through Ohio and Texas. I would guess that if she should lose those two big states, then I think that's when you'd see a reassessment, but not before then.

SMITH: Alright, Bob Schieffer, as always a pleasure to see you. We will see you on "Face the Nation" this weekend.

SCHIEFFER: Thank you.

Audio available here (23 seconds). 

—Kyle Drennen is a news analyst at the Media Research Center.