Hillary Clinton's closing moments of her latest debate with Barack Obama, where she said she was "honored" to be on stage with him and shook his hand, were roundly praised by her campaign. But in them, the Obama campaign saw similarities to the concession speech of their former rival John Edwards.

The Clinton lines came at the end of a debate Thursday in Austin, Texas, that offered few fireworks, as the two candidates took a measured approach to outlining their differences over health care, foreign policy and leadership. Heading into the crucial March 4 primaries in Texas, Ohio and two other states, Clinton has lost 11 consecutive contests and steadily has watched her delegate lead slip away.

"And, you know, no matter what happens in this contest ... I am honored to be here with Barack Obama. I am absolutely honored," Clinton said in her closing, before reaching over to accept a handshake from him. "Whatever happens, we're going to be fine. You know, we have strong support from our families and our friends. I just hope that we'll be able to say the same thing about the American people, and that's what this election should be about."

The audience gave a standing ovation and applauded. Her spokesman said it showed her strength and compassion. Her husband said it showed off the real Hillary Clinton.

But minutes later, Obama spokesman Bill Burton sent around a memo excerpting the line, alongside two similar lines from former candidate Edwards. One of those passages came from the former North Carolina senator's concession speech in New Orleans Jan. 30.

After announcing he was suspending his campaign, Edwards said: "But I want to say this to everyone: With Elizabeth, with my family, with my friends, with all of you and all of your support, this son of a millworker's gonna be just fine. Our job now is to make certain that America will be fine."

The subject of the memo was "Clinton's 'best moment' someone else's line?" It was a clear attempt to suggest she was lifting lines from Edwards, and suggested similarities between Clinton's closing moments and Edwards' humble valedictory speech.

Clinton had jabbed at Obama during the debate for lifting lines from Massachusetts Gov. Deval Patrick. Clinton drew "boos" from the crowd when she ridiculed him as the candidate of "change you can Xerox."

The New York senator is banking a comeback on strong performances in delegate-rich Texas and Ohio. But even Bill Clinton has said if she can't win Texas she probably can't win the nomination. And polls show the Texas race suddenly in a dead heat.

Her remarks at the debate were "almost a quasi-concession speech," said Texas state Rep. Rafael Anchia, who backs Obama.

In a round of television appearances Friday morning, Clinton said her remarks were intended as "a recognition that both of us are on the brink of historic change."

"I'm very proud that we have the two of us in this contest seeking the Democratic nomination, hoping to become our next president," she said on CBS' "The Early Show."

She showed no signs of retreat, saying: "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, and I could step in and deal with the problems."

She is seeking to be the first female president, and Obama the first black president. Clinton worked hard during the debate to draw contrasts with Obama on issues, pressing her argument that Obama's health care reform proposal would leave 15 million people uninsured. Obama has countered that Clinton's plan, which requires everyone to carry insurance, would force people to purchase coverage they can't afford.

But otherwise, Clinton steered away from hard-hitting criticism of her rival. She agreed with him on most matters raised in the debate, including immigration policy and fixing the economy. She let pass a statement that he would be willing to meet with new Cuban leader Raul Castro "without precondition" after hammering him for making a similar comment in another debate last summer.

"She's somewhat boxed in: Play nice and let the Obamomentum continue, or sharpen the attacks and risk a backlash," said Dan Newman, a California-based Democratic strategist not affiliated with either candidate.

That's why the end of the debate and Clinton's generous praise of Obama stood out -- she offered the gesture after alluding to her husband's impeachment over his relationship with White House intern Monica Lewinsky.

"I think everybody here knows I've lived through some crises and some challenging moments in my life," she said, winning applause and cheers.

Clinton's remarks were described by her supporters as a moment of genuine compassion -- much like her emotional moment on the campaign trail shortly before she won the New Hampshire primary.

"What we saw in the final moments in that debate is why Hillary Clinton is the next president of the United States. Her strength, her life experience, her compassion. She's tested and ready. It was the moment she retook the reins of this race and showed women and men why she is the best choice," spokesman Howard Wolfson said in a statement.

Speaking about the debate in San Antonio, Bill Clinton said, "I loved it at the end when she looked over to Sen. Obama and she said, ‘I'm honored to run with you ... You don't have to be against anyone in this election, but you do have to pick the best president."

Asked what was his favorite part, Clinton said, "Oh, her closing. That's my girl. That's the person I've known."

Politico editor Jim VandeHei said he didn't think Clinton was trying to say good-bye in her closing remarks.

"I think she was trying to make it like ‘This isn't about me' ... I don't think it was necessarily a 'Good-bye; hey, I can't win this.'"

But he added: "She knows that this could be it."

The Associated Press contributed to this report.