WASHINGTON (CBSNewYork/AP) -- Republican presidential candidate Carly Fiorina finds herself in a position to build on a strong debate performance for the second time in six weeks, enjoying rave reviews for demonstrating a command of policy details, while also taking on front-runner Donald Trump in last night's face-off.
"Going into that debate half the audience had never heard my name and didn't know I was running for president, so it was a big opportunity for me to introduce myself to many of the American people, and I'm very happy I had that opportunity," Fiorina told "CBS This Morning" on Thursday, just hours after the conclusion of the debate at Ronald Reagan's presidential library.
Fiorina, the only woman among Republicans' 15 top candidates, offered forceful answers Wednesday on U.S. relations with Russia and funding for women's health and abortion provider Planned Parenthood, among other topics. But one of her standout moments came when she dismissed Trump's previous criticism of her appearance.
"I think I made my point crystal clear, and I think women in America understand that it is still different for women, that we're scrutinized differently," she said. "The truth is that a woman's appearance should never be the subject of conversation, particularly in a presidential campaign."
Trump, for his part, told NBC on Thursday that "Carly did well,'' though he said he doesn't think the lengthy session had a singular standout.
Unlike Fiorina, who was praised Thursday morning for her grasp of policy, Trump offered little of substance in his answers.
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"I consider climate change to be not one of our big problems,'' Trump said Thursday, when asked about the debate's concluding exchange on climate change. "There could be some man-made something,'' he added.
He faced a series of attacks from his rivals on the stage, who were eager to try and bring his numbers down after watching the billionaire businessman rise in the polls.
Former Florida Gov. Jeb Bush, who was more aggressive against Trump than during the first debate in August, said he is pleased with his performance.
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"I'm not a Trumpian; I can't figure the guy out,'' Bush told NBC in a taped interview broadcast Thursday morning. "I took him on ... and I'll keep doing it. ... I'll fight back.''
Initially viewed as a front-runner, the former Florida governor has struggled to turn his commanding fundraising advantage into voter support.
"Everybody knows me as George's boy and George's brother, of which I'm proud,'' Bush said, but "I've got to tell that story'' of a "conservative record'' as Florida governor. "I'm confident I'll pick up steam going forward.''
New Jersey Gov. Chris Christie emphasized his and Bush's defense of President George W. Bush. Jeb Bush said his brother, often criticized for his decision to invade Iraq in 2003, "kept us safe'' after the attacks of Sept. 11, 2001. Christie stood by his remarks when asked Thursday on CNN whether George W. Bush's record is tainted by having been president at the time of the attacks.
While Christie got far less time in the debate than the front-runners, speaking for just a little more than 11 minutes during the three-hour session, he attempted to make the most of his time by targeting Trump and Fiorina for focusing on their business records.
"They weren't doing proof points last night with each other. What they were doing was getting in the typical personal food fight," Christie told "CBS This Morning." "In the first debate, it was between Jeb and Donald Trump. Then yesterday it was between Donald Trump and Carly Fiorina, and they were going tit for tat with each other. That adds nothing to people's knowledge about what kind of president you would be."
The political world is wondering if voters are ready to say "you're fired" to Trump.
Republican political consultant Frank Lutz tracked the reactions of voters to Trump's debate performance. He told "CBS This Morning" that when Trump was on the attack, voter approval went down.
"They were very disappointed that too often he seemed to take personal shots at the people to his left and to his right, rather than focusing on the question and answering the specifics of, 'What do you with Russia?' and 'What do you do with ISIS?'" Lutz said.
Speaking to CBS2's Marcia Kramer, celebrity and business media coach Ruth Sherman had this assessment: "I think last night is the beginning of the end for Trump. That is my prediction. I've been wrong before, but I do believe people are starting to see through some of the bluster and bombast."
Christie said his strategy at the debate was "just to be myself."
"In a field this crowded, what you really need to do is let people know you, be yourself," he said. "That's what I tried to do last night and focus on the problems that the people that were actually watching the debate rather that focusing on the arguments between all the people at the debate."
Several pundits felt the big winner was Fiorina, not only because of her command of the issues but also how she dealt with Trump saying, "Look at this face. Would anyone vote for that?"
"I think women all over this country heard very clearly what Mr. Trump said," she said.
Fiorina also scored by being the only candidate who said she wouldn't put a woman on the face of $10 bill, saying in an interview later that "people are tired of empty gestures."
"Carly Fiorina came out ahead just like she did the last time," Sherman said. "She was assertive and she's able to communicate what she has in her mind out through her mouth without a lot of 'uhs' and 'ums' and a lot of hesitations."
In her interview, Fiorina downplayed her place as the only woman among the top Republican hopefuls, saying, "I've never been a token in my life.'' But GOP strategists and voters are increasingly intrigued about Fiorina as an obvious foil to Democratic hopeful Hillary Rodham Clinton.
"Hillary Clinton is going to have to stand to account for her track record and her accomplishments, or lack thereof," Fiorina said. "That's what this election should be about."
Fiorina also faces increasing focus on her record, with new attention on her rocky tenure at Hewlett-Packard, where she was ultimately fired. Mostly repeating the answer she offered Wednesday, Fiorina told NBC that the experience is not a liability.
There are 10 more Republican debates. The next one is late next month in Colorado.
There are also six Democratic primary debates on the horizon.
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