From businessman Donald Trump's slam on O'Donnell to Gov. Chris Christie (R-N.J.) and Sen. Rand Paul (R-Ky.) getting into it over hugs, here are some of the most memorable moments from first Republican presidential debate. (Fox News Channel)

Donald Trump landed on the Republican debate stage like a hand grenade here on Thursday night — serving notice that he may run as an independent if he does not get the party’s nomination, dismissing criticism of his insulting comments about women as “political correctness” and flatly calling the nation’s leaders “stupid.”

The current leader of the GOP pack drew boos and cheers from the audience and set the tone for a raucous two-hour debate. And other candidates acknowledged that Trump, a celebrity billionaire known for his showman’s flair, has tapped into a genuine current of public outrage and exasperation.

“Donald Trump’s hitting a nerve in this country. He is. He’s hitting a nerve,” Ohio Gov. John Kasich said. “People are frustrated, they’re fed up, they don’t think the government’s working for them. People who want to tune him out are making a mistake.”

Only 10 of the 17 declared contenders for the 2016 GOP nomination appeared in the first official debate of the 2016 campaign season. They were chosen by debate sponsor Fox News Channel because they ranked highest in the polls, though some of them are barely registering.

Trump’s entry into the race — and his continuing rise despite a series of incendiary comments — has thrown into chaos a party that is normally known for a coronation-like orderliness in its nominating process.

A first-time candidate, Trump is overshadowing the bids of a host of current and former governors and senators. And he is undercutting party leaders’ hopes of upgrading the GOP’s image by presenting a field of candidates distinguished by their experience, policy expertise and gravitas.

The internecine battle also is shifting focus from making their larger case against the Democratic front-runner, former secretary of state Hillary Rodham Clinton, at a time when her poll numbers are sinking.

“Let’s be clear, we should be talking about Hillary Clinton . . . because everywhere in the world that Hillary Clinton touched is more messed up today than before,” Wisconsin Gov. Scott Walker said.

The moderators’ questioning of Trump was particularly aggressive.

“The questions to me were not nice. They were inappropriate,” Trump told reporters after the debate. “But you know what? The answers were good, obviously, because everyone thinks I won.”

Trump was asked to explain the bankruptcies of his companies (he responded that he simply used bankruptcy laws to maximum advantage); to detail his evidence that the Mexican government was sending criminals over the border (he said U.S. Border Patrol agents had told him so); why he once supported a single-payer health-care system (he said it worked well in Canada and Scotland); what favors he received for his campaign donations to Hillary Rodham Clinton (he said she showed up at his wedding on demand); and when he became a Republican (he did not say).

The GOP debate, charted word by word

In one particularly vivid exchange, Fox News’s Megyn Kelly noted that Trump had referred to women with whom he had disagreed as “fat pigs, dogs, slobs and disgusting animals.”

After interrupting with “Only Rosie O’Donnell,” referring to a celebrity with who he has feuded, Trump replied more fully: “I’ve been challenged by so many people, and I don’t frankly have time for total political correctness. And to be honest with you, this country doesn’t have time either.”

He also minimized his comments as “fun, it’s kidding. We have a good time. What I say is what I say. And honestly, Megyn, if you don’t like it, I’m sorry. I’ve been very nice to you, although I could probably maybe not be, based on the way you have treated me.”

It was pointed out that, if he follows through on his threat to run as an independent, Trump could doom the Republican Party’s chances of victory in 2016. Trump noted that gives him “a lot of leverage.”

Sen. Rand Paul (Ky.) jumped in, portraying that attitude as political treason: “Hey, look, look! He’s already hedging his bet on the Clintons, okay? So if he doesn’t run as a Republican, maybe he supports Clinton, or maybe he runs as an independent, but I’d say that he’s already hedging his bets because he’s used to buying politicians.”

Trump appeared to set the tone for a debate that was combative throughout on a range of issues.

New Jersey Gov. Chris Christie and former Arkansas governor Mike Huckabee disagreed sharply over changes to Social Security and other entitlements. Christie argues that fiscal realities make cutbacks inevitable, while Huckabee has insisted that the safety net for the elderly must be preserved.

Christie also sparred with Paul over the National Security Agency surveillance program authorized under the USA Patriot Act.

The New Jersey governor said the federal government needs more tools, not fewer, to root out terrorism and protect the homeland, while Paul cited the Bill of Rights in calling for scaling back spying programs.

“I want to collect more records from terrorists, but less records from innocent Americans,” Paul said.

Christie retorted, “That’s a completely ridiculous answer,” and added that Paul’s experience on national security matters consists of “blowing hot air” on a congressional subcommittee.

Former Florida governor Jeb Bush, for better or worse, largely steered clear of the fray.

At one point, Trump turned to Bush and disparaged his brother, former president George W. Bush: “The last couple of months of his brother’s administration were a catastrophe.”

Bush did not directly respond, instead trying to rise above his opponent to say Republicans cannot win back the White House by “dividing the country and creating a grievance kind of environment.”

Trump then called Bush “a true gentleman” but said that his admonishment of Trump’s “tone” was misplaced.

“When you have people that are cutting Christians’ heads off, when you have a world at the border and at so many places that it’s medieval times . . . we don’t have time for tone,” Trump said. “We have to go out and get the job done.”

Sen. Ted Cruz of Texas took a similarly sharp tone on the subject of illegal immigration, saying he supports legislation — inspired by last month’s death of Kathryn Steinle in San Francisco, who allegedly was killed by an undocumented immigrant — to defund “sanctuary cities,” or jurisdictions that defy federal authorities in order to protect immigrants living in the U.S. illegally.

“You know, there was reference made to our leaders being stupid,” Cruz said, referring to Trump’s comments. “It’s not a question of stupidity. It’s that they don’t want to enforce the immigration laws. That there are far too many in the Washington cartel that support amnesty.”

The Republicans voiced outrage over recently surfaced clandestine videos of Planned Parenthood employees discussing the harvesting of organs from aborted fetuses.

“I think future generations will look back to this history of our country and call us barbarians for murdering millions of babies because we never gave them a chance to live,” said Sen. Marco Rubio (Fla.), who emphasized his opposition to abortion, including in cases of rape and incest.

Huckabee used more vivid language, saying the country must change its policies to “protect children instead of rip up their body parts and sell them like they’re parts to a Buick.”

The Fox moderators put Bush on the defensive over his role on the board of former New York mayor Michael R. Bloomberg’s charitable foundation, which supported Planned Parenthood. Bush declared, “My record as a pro-life governor is not in dispute,” and he boasted that he defunded Planned Parenthood and directed state funds to crisis pregnancy centers.

A political newcomer, retired neurosurgeon Ben Carson, has been popular on the hustings but garnered little attention Thursday night.

The first question he got was about his lack of foreign policy credentials — a point he conceded. “In fact, the thing that is probably most important is having a brain, and to be able to figure things out and learn things very rapidly,” Carson said. “You know, experience comes from a large number of different arenas.”

Rubio also deflected a question about his lack of executive experience by saying the election would not be a “résumé competition” but rather about which candidate best represents the future.

“If I’m our nominee, how is Hillary Clinton going to lecture me about living paycheck to paycheck?” Rubio said. “I was raised paycheck to paycheck. How is she going to lecture me about student loans? I owed over $100,000 just four years ago.”

Kasich, a recent entrant into the race, sought to make the most of his turn on the main debate stage. He delivered impassioned defenses of his expansion of Medicaid in Ohio to help lift up the poor as well as on gay rights. He said that although he personally opposes same-sex marriage, he accepts the Supreme Court’s ruling as the law of the land, recently attended a friend’s gay wedding and would love his daughters if they were lesbians.

The Republicans had particularly sharp criticism of Obama’s foreign policy, including his handling of the growing threat of Islamic State terrorists and the administration’s negotiation of a nuclear deal with Iran.

“We are leading from behind under the Obama-Clinton doctrine,” Walker said. “America’s a great country. We need to stand up and start leading again, and we need to have allies — not just in Israel, but throughout the Persian Gulf.”

David Weigel contributed to this report.