Las Vegas (CNN) The simmering rivalry between Marco Rubio and Ted Cruz spilled into the open Tuesday night during the final Republican presidential debate of the year, as the two senators tussled over a string of issues that served to highlight front-runner Donald Trump's discomfort with policy substance.

CNN's two-hour prime-time event here was dominated by national security and terrorism in the aftermath of the deadly terrorist attacks in Paris and San Bernardino, California.

But Trump, who has fueled intense controversy by proposing a ban on Muslims entering the United States, often faded into the background. He even struck an uncharacteristically conciliatory tone by pledging his commitment to the Republican Party -- putting to rest rumors of an independent run -- and holding his punches from the surging Cruz.

There was no one on stage more eager to hit Trump than Jeb Bush. With his campaign floundering as his poll numbers have dropped to the low single-digits, Bush asserted himself more effectively than in previous debates. Right out of the gate, the two men exchanged tense words on Trump's plan Muslim ban proposal, as well as the real estate developer's recent vow to go after family members of ISIS terrorists.

The latter, Bush said, was "another example of (Trump's) lack of seriousness."

Trump, visibly annoyed, mouthed: "Give me a break." He delivered his usual attack line on the ex-governor: that he is simply too nice.

"I think Jeb is a very nice person, very nice person," Trump said. "But we need toughness."

When Bush interjected, Trump taunted: "You're trying to build up your energy but it's not working."

Bush shot back: "Donald, you're not going to be able to insult your way to the presidency."

GOP prime-time debate verbal attacks:

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Digging deep on policy

In stark contrast to Trump and Bush's open personal hostiliy -- which at times seemed petty against the backdrop of weighty issues like terrorism -- Rubio and Cruz dug deep on policy.

The long-simmering feud between the two men has intensified as they've risen in the polls and the senators have sought to seize the second-place spot after Trump. Cruz has attempted to straddle the line between presenting himself as an outsider and making the case that he can be commander-in-chief. Rubio has tried to blunt Cruz's rise by attacking his national security policy as too isolationist -- a potent attack at a time when national security is dominating the campaign.

The two senators struck vastly different tones on issues including the National Security Agency's surveillance program, immigration reform and how the United States should respond to dictators in the Middle East. Rubio blasted Cruz for voting for the USA Freedom Act, which made it more difficult for the government to access certain kinds of information about people's telephone records.

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"Here's the world we live in. This is a radical jihadist group that is increasingly sophisticated," said Rubio, who voted against the act. "We are at a time when we need more tools, not less tools."

Cruz called Rubio's accusation false, and said the law ultimately "strengthened the tools of national security and law enforcement to go after" terrorists.

He also hit Rubio on one of his biggest political vulnerabilities: his work on the "Gang of Eight" comprehensive immigration reform bill. Calling the legislation a "massive amnesty plan," Cruz accused Rubio of working with Democrats to give President Barack Obama a "blanket authority" to accept refugees.

"He was fighting to grant amnesty and not to secure the border. I was fighting to secure the border," Cruz said.

Rubio hit back, saying Cruz supports the legalization of people who are in the country illegally. He also slammed his colleague for supporting a controversial H-1B visa program, which supports immigration of highly skilled foreign workers.

Cruz and Rubio were also split on whether the turmoil in the Middle East would ease if Syrian President Bashar al-Assad was removed from power.

"If we topple Assad, the result will be ISIS will take over Syria and it will worsen U.S. national security interests," Cruz said.

Rubio rejected this notion, saying while the United States must sometimes work with "less than ideal governments," Assad was simply an "anti-American dictator."

Photos: Who's running for president? Photos: Who's running for president? Ted Cruz, Donald Trump, John Kasich, Hillary Clinton and Bernie Sanders, Hide Caption 1 of 6 Photos: Who's running for president?



"So, ladies and gentlemen, I am officially running for president of the United States, and we are going to make our country great again," Trump told the crowd at his announcement. Businessman Donald Trump announced June 16 at his Trump Tower in New York City that he is seeking the Republican presidential nomination. This ends more than two decades of flirting with the idea of running for the White House."So, ladies and gentlemen, I am officially running for president of the United States, and we are going to make our country great again," Trump told the crowd at his announcement. Hide Caption 2 of 6 Photos: Who's running for president?



"These are all of our stories," Cruz told the audience at Liberty University in Virginia. "These are who we are as Americans. And yet for so many Americans, the promise of America seems more and more distant." Sen. Ted Cruz of Texas has made a name for himself in the Senate, solidifying his brand as a conservative firebrand willing to take on the GOP's establishment. He announced he was seeking the Republican presidential nomination in a speech on March 23."These are all of our stories," Cruz told the audience at Liberty University in Virginia. "These are who we are as Americans. And yet for so many Americans, the promise of America seems more and more distant." Hide Caption 3 of 6 Photos: Who's running for president? Ohio Gov. John Kasich joined the Republican field July 21 as he formally announced his White House bid.



"I am here to ask you for your prayers, for your support ... because I have decided to run for president of the United States," Kasich told his kickoff rally at the Ohio State University. Hide Caption 4 of 6 Photos: Who's running for president?



"Everyday Americans need a champion, and I want to be that champion -- so you can do more than just get by -- you can get ahead. And stay ahead," she said in her announcement video. "Because when families are strong, America is strong. So I'm hitting the road to earn your vote, because it's your time. And I hope you'll join me on this journey." Hillary Clinton launched her presidential bid on April 12 through a video message on social media. The former first lady, senator and secretary of state is considered the front-runner among possible Democratic candidates."Everyday Americans need a champion, and I want to be that champion -- so you can do more than just get by -- you can get ahead. And stay ahead," she said in her announcement video. "Because when families are strong, America is strong. So I'm hitting the road to earn your vote, because it's your time. And I hope you'll join me on this journey." Hide Caption 5 of 6 Photos: Who's running for president?



"This great nation and its government belong to all of the people and not to a handful of billionaires, their super PACs and their lobbyists," Sanders said at a rally in Vermont on May 26. Sen. Bernie Sanders , an independent from Vermont who caucuses with Democrats, announced his run in an email to supporters on April 30. He has said the United States needs a "political revolution" of working-class Americans to take back control of the government from billionaires."This great nation and its government belong to all of the people and not to a handful of billionaires, their super PACs and their lobbyists," Sanders said at a rally in Vermont on May 26. Hide Caption 6 of 6

High stakes after terror attacks

Heading into Tuesday's debate, the stakes were higher than ever for the White House hopefuls.

The Iowa caucuses are just seven weeks away and ISIS-inspired terror attacks have shifted the dynamics of the 2016 campaign. The anxiety was evident on Tuesday when public schools in Los Angeles took the unprecedented step of closing in response to what the superintendent called a "rare" threat.

Trump remains the undisputed national GOP presidential front-runner. A Monmouth University poll on Monday placed him at 41% , the first time he's cracked the 40% threshold in a national survey. A poll from The Washington Post and ABC News conducted entirely after Trump proposed the Muslim ban found support for Trump at 38% of Republicans and Republican-leaning independents -- up six percentage points from a Post/ABC poll in mid-November.

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Trump does, however, face a real threat from Cruz in Iowa. Recent polls showed the senator either neck-and-neck with or ahead of Trump in the state.

On Tuesday night, Cruz continued to show little appetite for publicly engaging Trump. Asked to respond to Trump's Muslim ban proposal, the Texas senator said he could certainly "understand why Donald made that proposal."

Criticism from underdogs

Trump was the target of plenty of criticism during the earlier so-called "undercard" debate. Four lower-polling White House hopefuls kicked off the evening by raising alarm about the threat of radical Islam -- and went after Trump for the Muslim proposal.

"You may think this makes us safe, but it doesn't," said South Carolina Sen. Lindsey Graham, one of Trump's most vocal critics. "Donald Trump has done the one single thing you cannot do -- declare war on Islam itself."

Former Pennsylvania Sen. Rick Santorum said it's "not the right proposal."

But Santorum blasted a culture of political correctness that he faults for blunting debate over the role of Muslims in society.

"Not all Muslims are jihadists," he said. "All jihadists are Muslim."

Santorum and Graham -- who dominated the discussion -- were joined by former Arkansas Gov. Mike Huckabee and former New York Gov. George Pataki. All four are at risk of being next on the chopping block if they're unable to gain real momentum soon.