Republican presidential candidate Donald Trump, whose caustic comments about Mexicans have inflamed the immigration debate, told thousands of cheering supporters here Saturday that “we have to take back the heart of our country.”

In a rambling, defiant speech delivered in this border state that has been the epicenter of the nation’s divisive battle over immigration reform, Trump declared: “These are people that shouldn’t be in our country. They flow in like water.” One man in the crowd of 4,200 shouted back, “Build a wall!”

Basking in polls that show he has risen to the top of the crowded Republican field, Trump took obvious glee in mocking former Florida governor Jeb Bush, the establishment favorite who is setting fundraising records.

“Jeb Bush, let’s say he’s president — Oy, yoy, yoy,” Trump said. He asked the crowd: “How can I be tied with this guy? He’s terrible. Terrible. He’s weak on immigration.”

Trump’s 70-minute address here, which sounded more like a stream-of-consciousness rant than a presidential-style stump speech, put an exclamation point on his bombastic push since his presidential announcement last month to return immigration to the forefront of the national conversation.

Republican Presidential candidate Donald Trump addresses supporters during a political rally in Phoenix on Saturday. (Charlie Leight/Getty Images)

Bush and illegal immigrants were not the only targets of Trump’s scorn: He also criticized Macy’s, NBC, NASCAR, U.S. ambassador to Japan Caroline Kennedy, Democratic presidential candidate Hillary Rodham Clinton and, several times, the media.

Republican leaders say they believe the celebrity billionaire has virtually no chance of being their nominee, much less of making it to the White House. And, for now at least, his following seems limited to the far right as opposed to the party’s mainstream.

Yet Trump has reignited a heated debate over an issue, immigration, that the GOP had been determined to settle after it hurt Republicans in the most recent presidential election.

Party leaders increasingly fear that Trump could do damage to more viable candidates, such as Bush, who could lose their own footing on immigration. These candidates confront a familiar challenge: During the primary season, they must deal with the anger and anxiety that many on the right feel about illegal immigration. But they must do it in a way that will not damage their appeal to a broader electorate in November 2016.

Republicans are handling Trump delicately for another reason as well: They fear that he could leave the GOP entirely and wage a well-funded third-party campaign, a possibility that Trump has not ruled out.

After Trump repeatedly referred to illegal immigrants in the harshest of terms — calling them, among other things, killers and rapists — Republican National Committee Chairman Reince Priebus called Trump and asked him to tone things down. But that, if anything, has reinvigorated Trump and his vocal supporters.

The crowd in Phoenix began lining up outside the convention center before dawn, with many spending hours in temperatures that exceeded 100 degrees. Hundreds of people, who stood in lines snaking down several downtown blocks, did not make it into the ballroom for his speech.

Many of Trump’s supporters blame illegal immigrants for crime and economic problems but also express dismay over cultural changes.

“We don’t recognize our country anymore,” said Jan Drake, 72, who lives in a retirement community outside Phoenix. “If you’re coming into our country, you have got to conform to what we stand for. You speak English. You don’t try to change our country to what your country was.”

After watching Trump on television the past couple of weeks, Drake said that she has become convinced that “he would be a very strong president. He doesn’t kowtow to anybody. The Republican Party will try to squeeze him out because they’re afraid of him. But he can tell them where to go — to pound sand.”

After he walked onto a catwalk stage here like a rock star, Trump basked in his crowd. “The word is getting out that we have to stop illegal immigration,” he said.

While Trump was railing against Spanish-language broadcaster Univision, a handful of protesters in the crowd interrupted. Trump’s security guards arrived to break up the skirmish that followed. His supporters screamed “USA! USA! USA!” in the protesters’ faces as the guards escorted them out of the convention hall.

“I wonder if the Mexican government sent them over here,” Trump said from the stage. He assured the crowd, “Don’t worry, we’ll take our country back.”

Trump also had harsh words for Islamic State terrorists. If he becomes president, Trump said, “They will be in such trouble . . . ISIS, believe me, I would take them out so fast. You have to do it.”

But it was his crusade against illegal immigrants that had Trump’s crowd most enthused. After expressing shock that his immigration message has resonated so strongly with the GOP base, Trump said, “The silent majority is back, and we’re going to take the country back.” He walked off the stage to Twisted Sister’s “We’re Not Gonna Take It.”

Earlier, as his plush Boeing 757 headed from an appearance in Las Vegas to Phoenix, Trump sat in a leather chair, surrounded by binders of articles about him and sipping a Coca-Cola — the full-calorie kind, he noted, because, “Have you ever seen a thin person drinking Diet Coke?”

“Something is happening in America. You may not want to see it, but something big is happening. People are sick and tired of politicians, and I’m here for them,” he said in an interview. “I’m ready to go right at the Mexican government. I’m going to charge them $25,000 per illegal immigrant and, oh, I’ll make them pay.”

(In his Phoenix speech, Trump put the figure at $100,000.)

“Would Bush do that? Would Rubio? I don’t think so,” Trump added, taking aim at two of his more mainstream rivals, Bush and Sen. Marco Rubio (R-Fla.).

Polls consistently show that a majority of Americans, including most Republicans, support an overhaul of the law to give millions of undocumented immigrants a means of staying in this country legally. But a passionate fraction of the Republican electorate believe otherwise.

Lou Brudnock, 71, said he is attracted to Trump’s brash “truthfulness” on immigration and his willingness to be politically incorrect.

“This country today is sad, sad, sad,” Brudnock said. “You can’t say anything or they call you ‘a racist.’ It’s like we’re back in Nazi Germany. But look around, man. It’s people here reading and listening to his message.”

Trump, by virtue of his celebrity, has provoked a backlash far more widespread than ever seen toward lesser-known immigration hard-liners, such as former Colorado congressman Tom Tancredo (R). That means he could leave lasting damage to the GOP and whoever turns out to be its 2016 standard-bearer.

All of those cross-pressures were in play Saturday at Trump’s appearances here and in Las Vegas. More mainstream Republicans had anticipated the spectacle and made no secret of their concern.

“I had hoped that we had moved on from some of the coarse rhetoric,” said Sen. Jeff Flake (R-Ariz.). “When there’s so many candidates, you can appeal to a very small segment of the population and get news and get elevated.” Flake is a leading proponent of a comprehensive immigration measure that would include a path to citizenship for those who are in the country illegally.

Arizona has been a hotbed of anti-immigration sentiment, having passed a 2010 law that requires law enforcement officials to check the immigration status of people they detain and suspect are in the country illegally.

Maricopa County, Ariz., Sheriff Joe Arpaio — who in some ways is the face of that law, having been the subject of racial-profiling lawsuits — helped warm up the crowd before Trump’s arrival.

“I know that Donald Trump is speaking out,” Arpaio said. “He’s getting a lot of heat. But, you know, there’s a silent majority out here.”

“We’re not silent anymore!” a man in the crowd shouted.

Arpaio brought up the mostly dormant questioning of President Obama’s birth certificate. He and Trump are perhaps the most vocal of the “birthers,” who falsely contend that Obama was not born in the United States.

Immigration also has gained new attention after the June 30 shooting death of a woman along San Francisco’s heavily touristed waterfront, allegedly by an illegal immigrant who had been deported five times from the United States.

Trump — along with much of the rest of the Republican field — has criticized the policies of “sanctuary cities,” where officials cannot detain those they suspect of being in the country illegally unless they have other grounds to do so.

Republican strategists say that it is possible to address anxiety over illegal immigration within the GOP base without alienating the electorate at large. Advisers to Bush and Rubio, for instance, say that their candidates can play a long game on the issue, continuing to make a case for comprehensive changes to the law, while waiting for the Trump boomlet to subside.

“You can give a fuller picture of those types of people who are coming to America who are not documented, who are not legal,” said Peter Wehner, who was a top official in George W. Bush’s White House. “And you can speak about them in a humane and decent and true way.”

Karen Tumulty in Washington contributed to this report.