ANALYSIS: As Presidential Race Gets Bigger, Donald Trump Goes Smaller

The death of Justice Scalia raised the stakes of a presidential campaign.

Bush fired back: "I'm sick and tired of Barack Obama blaming my brother for all of the problems that he's had. I'm sick and tired of [Trump] going after my family."

John Kasich summed up the back-and-forth: "I got to tell you, this is just crazy. This is just nuts."

Trump's fight with Cruz was even sharper.

"You are the single biggest liar. You probably are worse than Jeb Bush," Trump said of Cruz. "This guy will say anything. Nasty guy."

Cruz called Trump a liberal, and added this: "Donald, adults learn not to interrupt each other."

Predictions of Trump doing damage to his own campaign have been almost comically wrong over the past six months. Trump knows his followers, up to and including their antipathy for the Bush family.

But the Bush name still carries weight among South Carolina Republicans, in a story line that will be enhanced Monday with the expected campaign debut of George W. Bush. It's equally plausible to imagine Republicans growing sick of the name-calling, particularly as Scalia's death highlights the stakes of the race anew.

Bush was also able to rise above a sharp battle between Rubio and Cruz, on the now-familiar topic of immigration. They accused each other of misleading on their records; Rubio went so far as to say Cruz "doesn't speak Spanish," and Cruz offered to switch over to some "espanol."

Rubio picked up the anti-Cruz mantle, in a debate where he came out more aggressive -- and less repetitive -- than a week ago.

"This is a disturbing pattern now. For a number of weeks now, Ted Cruz has just been telling lies," he said.

Trump, of course, wasn't stopping –- not in a debate where he sought out fights with his rivals, notwithstanding his front-running status. Toward the end of the debate, he vowed to stop using bad words, which he said would be easy because he was "a very good student at a great school."

Perhaps Trump is indeed a better student than everyone in the political class has realized. That's been a recurring theme of this campaign, much to the frustration of his rivals.

But on a night where the importance of the race was highlighted anew, Trump’s rivals could portray him as flunking a big test.