Republican presidential candidate Carly Fiorina, seen being interviewed before speaking Friday in Atlanta at the RedState Gathering, calls her debate appearance a win. (David Goldman/AP)

Carly Fiorina took the stage at a conservative summit here Friday to a standing ovation, her first of four. She smirked and said: “I think we kind of won last night. What do you think?”

Fiorina spent the day traveling, bouncing between television interviews, taking selfies, fielding calls from giddy supporters and trying to capi­tal­ize on her highly praised performance in a debate for lower-tier Republican presidential candidates Thursday night.

The moment was months in the making for Fiorina, the former chief executive of Hewlett-Packard who launched a long-shot bid that has yet to gain traction in early polls. She has pitched herself as the GOP’s lone woman who can mercilessly criticize Democratic front-runner Hillary Rodham Clinton — and joke about hormones in the White House — without being accused of sexism. She has tied some of her campaign stops to Clinton’s schedule and, at times, has seemed to play up her femininity, picking sundresses over suits, pink over black.

But Fiorina emerged from Cleveland on Thursday independent of her female foil, suggesting she can play a greater role in the crowded GOP field as a fearless debater not afraid to go after candidates in either party.

“I’ve also gained a reputation, maybe, for saying some things that other people aren’t prepared to say,” Fiorina said at the RedState Gathering, a summit hosted by a popular conservative Web site.

In a sense, Fiorina has something in common with Donald Trump, the bombastic real estate magnate and television celebrity who has vaulted to the top of early GOP polls. Neither has ever held an elected office, and both pitch themselves as Washington outsiders who would bring their business sense to the White House. And although both have been firing off fierce attacks on the campaign trail, Fiorina does so with more finesse, composure and control.

Fiorina is not afraid to go after Trump — and he’s the only candidate to have gone after her, mocking her embarrassing departure from Hewlett-Packard and discrediting her viability. On Thursday evening, Fiorina was asked why Trump was doing so much better than her in the polls.

“Well, I don’t know, I didn’t get a phone call from Bill Clinton before I jumped in the race,” Fiorina said sarcastically, referring to a conversation about politics between Trump and the former president. “Did any of you get a phone call from Bill Clinton? I didn’t.”

Fiorina commended Trump for tapping into the anger of voters who are “sick of politics as usual.”

But then she went after his conservative credentials, noting that he has changed his stances on immigration, health care and abortion.

“What are the principles by which he will govern?” Fiorina said at the debate, which happened hours before Trump took the stage at the prime-time debate with the top 10 competitors.

So far, Fiorina’s lack of name recognition has had its advantages, allowing her to provide her own narrative of her little-known life.

She routintely says that she started as a secretary in a small real estate firm — actually a short-term, post-college gig that came before a European journey — and worked her way up to becoming the top executive at Hewlett-Packard, rarely mentioning her controversial ouster from the company. And there’s the last political campaign she tried, when she was trounced in an unsuccessful run for the U.S. Senate in California.

But with her debate performance came new scrutiny.

Democratic National Committee Chairwoman Debbie Wasserman Schultz, for example, sharply attacked Fiorina’s business record Friday on MSNBC’s “Morning Joe.”

“What’s impressive about a woman who nearly drove a Fortune 500 company into the ground?” Wasserman Schultz asked. “Who fired 30,000 people when she was CEO? Whose stock dropped by 50 percent when she was the head of a company and then recovered after she was fired by 10 percent?”

But the DNC is also facing criticism for a tweet from Thursday that read: “Fiorina says her business experience prepared her to be president. But under her ‘leadership,’ HP stock fell 53%.” Attached was an animated image of a young girl wearing pink and pigtails who shrugged. Social media quickly filled with accusations of sexism.

Here on Friday afternoon, a reporter asked Fiorina why she criticized Trump for being cozy with the Clintons when she was a featured speaker at an event hosted by the Clinton Global Initiative. Fiorina’s eyes narrowed as she stared down the reporter.

“So, you really don’t understand the difference between getting a personal phone call from Bill Clinton and showing up at a conference?” she said.

Other GOP candidates have refrained from criticizing Fiorina, with several instead lavishing praise on her. But that could stop if she keeps up her attack on GOP rivals.

An early testing of the waters: Fiorina went after former Florida governor Jeb Bush on Thursday evening, criticizing him for stumbling on the campaign trail with remarks on women’s health funding and giving “Democrats an ad and a talking point before he’s even in the ring.”

But Fiorina’s sharpest swipes — and her most biting jokes — are reserved for the other woman angling for the presidency. At the debate, Fiorina accused Clinton of having lied as secretary of state about the 2012 attacks in Benghazi, Libya, as well as other issues.

That became the focus of an interview Fiorina did that night as a guest on MSNBC’s “Hardball with Chris Matthews” — a show many Republicans avoid in favor of Fox News Channel appearances. Matthews asked Fiorina why she would paint a possible opponent as an all-out liar.

“I was very specific, very fact-based — actually, you were the one who has made a generalized comment about her,” Fiorina said, refusing to let Matthews cut back in while rattling off critiques of Clinton.

Some of Fiorina’s most devoted followers point to that interview as more of a success than the debate.

They add it to other events from the past few months — well-received speeches in Iowa, a long receiving line after a GOP fundraiser and a growing following in New Hampshire — that have earned her buzz in political circles but no appreciable movement in the polls.

Fiorina is taking “a long-term view of this race” and has already shown great potential, according to a strategy memo released Friday by a super PAC supporting her candidacy. Her biggest challenge: increasing her name recognition. Heading into the debate, Fiorina said only 40 percent of voters had heard her name.

“When you’re not a professional politician, when you’re not a celebrity, I started this campaign on May 4 almost from a standing start,” she said Friday. “And let’s face it, a lot of people probably underestimated me.”

Philip Rucker in Cleveland and Robert Costa and Dave Weigel in Atlanta contributed to this report.