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CLEVELAND (CNN) -- Donald Trump's latest reality show roared into Ohio on Thursday night.

Within a few minutes of his first debate as a Republican presidential candidate, Trump ridiculed comedian Rosie O'Donnell and griped about his treatment by Fox News anchor Megyn Kelly. But it was his refusal to rule out a third-party presidential run -- a move that could deny Republicans the White House -- that drew gasps in the audience and sparked anger from his opponents.

"I mean, this is what's wrong. He buys and sells politicians of all stripes. He's already hedging his bet on the Clintons, OK?" said Kentucky Sen. Rand Paul.

The ever-unapologetic Trump then chastised the country for being too "politically correct."

"I've been challenged by so many people and I don't frankly have time for total political correctness," Trump quipped.

Explosive start

It was an explosive start to the first GOP debate in a campaign season already upended by Trump, the unfiltered and brash real estate magnate. It was immediately apparent that classic Trump showed up to the debate -- someone who pushes the boundaries and has no qualms about leveling personal attacks in public.

Kelly challenged Trump on some of his past comments about women.

"You call women you don't like fat pigs, dogs, slobs and disgusting animals," she said.

Trump quickly responded: "Only Rosie O'Donnell."

Meanwhile, immigration loomed large at the debate -- an issue that Trump claimed full credit for bringing to the nation's attention.

"If it weren't for me, you wouldn't be even talking about illegal immigration, Chris," Trump said to Fox News host Chris Wallace. "This was not a subject that was on anyone's mind until I brought it up at my announcement."

Former Florida Gov. Jeb Bush, who has been trailing in second place behind Trump in the polls, addressed the issue by stressing that he did not support "amnesty." His stance on what to do about the millions of undocumented immigrants in the country has dogged Bush.

"We need to be much more strategic on how we deal with border enforcement, border security," Bush said. "We need to eliminate the sanctuary cities in this country. It is ridiculous and tragic that people are dying because of the fact that local governments are not following the law."

Trump was smack in the center of the debate lineup. The lower tier of presidential contenders had their brief moment in the sun earlier Thursday at a debate in which Carly Fiorina delivered a memorable and polished performance.

High-stakes moment for Trump

But the prime-time debate attracted more attention and served as a particularly high-stakes moment for Trump, whose early dominance has both stunned -- and aggravated -- members of his own party. National Republican leaders have at times seemed unsure of what to make of the fact that such a no-filter politician with no obligations to the party could unexpectedly become the GOP's standard-bearer. The evening was also an opportunity for Bush to move past a shaky few days that included controversial comments about women's health care along with an uncomfortable performance at a New Hampshire candidate forum.

The open contempt for Trump was on full display at the earlier debate. It took only 11 minutes before candidates came out swinging against Trump.

Lesser-known contenders including former Texas Gov. Rick Perry and Fiorina slammed Trump, blasting the billionaire businessman's conservative credentials and friendly relationship with Hillary and Bill Clinton.

"I talked about Donald Trump from the standpoint of being an individual who is using his celebrity rather than his conservatism," said Perry, who has positioned himself as one of Trump's biggest antagonists on the trail. "How can you run for the Republican nomination and be for single-payer health care?"

For his part, Trump found ways to mock his rivals. When asked to address some of his businesses that went bankrupt, Trump pivoted to the financial woes of New Jersey -- a clear swipe at Christie.

"I had the good sense to leave Atlantic City, which by the way, Caesars just went bankrupt," Trump said, then gestured to Christie. "Chris can tell you."

Later in the debate, Bush cautioned that Trump's "divisive" language could be detrimental to the Republican Party.

"We're going to win when we unite people with a hopeful, optimistic message," he said.

A Bloomberg survey released Tuesday had Trump at 21%, handing him a double-digit lead over both Bush, who was at 10%, and Wisconsin Gov. Scott Walker, who was at 8%.

Trump, Bush, Paul and Walker were on the prime-time debate stage with Mike Huckabee, Ben Carson, Ted Cruz, Marco Rubio, Chris Christie and John Kasich.

Christie-Paul fued

At one point, the debate stage turned into