Editor's note: David Gergen is a senior political analyst for CNN and has been an adviser to four presidents. He is a professor of public service and director of the Center for Public Leadership at Harvard University's Kennedy School of Government. Follow him on Twitter: @David_Gergen
Las Vegas, Nevada (CNN) -- Mitt Romney walked into Tuesday night's Republican debate as the front-runner and, in my view, walked out in an even stronger position. But in retrospect, he and party leaders might wish they could have invoked the Las Vegas rule: What happens there stays there.
Romney has frequently been the best of the candidates as a debater. With the exception of Newt Gingrich, he has the firmest grasp of his arguments and knows better how to deploy his facts. While he doesn't convey much warmth, he does signal competence, especially on the economy.
But Tuesday night he showed more: He demonstrated that he could take a punch and then counterpunch with considerable skill. When he and Herman Cain clashed over Cain's 9-9-9 plan, Romney won the argument over state tax increases and stuffed Cain with his apples and oranges line. When Rick Perry launched his personal attack on Romney over illegal immigrants, Romney gave at least as good as he got. And he effectively held off both Perry and Rick Santorum when each of them tried to seize control of the microphone from him. All the while, Romney was better than the others on stage at periodically returning to a central theme: getting America growing again.
Perry won top honors Tuesday night as the most improved debater. As John King commented afterward on CNN, another stumbling performance might have knocked him out of contention -- but Perry was far better prepared and energetic.
This may be a singular view, but Cain struck me as having one of his weaker nights. As all of his rivals jumped on his tax plan, his defenses seemed only to leave a haze of confusion and uncertainty. Public support for his tax plan probably peaked Tuesday night and with that, his prospects seem even more problematic.
One other candidate deserves honorable mention: Michelle Bachmann. Her heartfelt support for women threatened with home foreclosure was far and away the most emotionally connective statement of the evening. Why can't more of these candidates show greater empathy toward people who are hurting in this economy? (By contrast, Romney had his worst moment when he seemed cold toward those in foreclosure troubles.)
But for those who watched this debate, what stood out more than the performance of any single candidate was the continual outbreak of fights and personal insults. Democrats are used to brawls, but not Republicans. Long ago, as Gloria Borger pointed out after the debate, Ronald Reagan often invoked what he called the 11th Commandment for the GOP: Thou shalt not speak ill of another Republican.
The candidates trampled all over that commandment Tuesday night. GOP leaders must have been horrified. Who can remember a debate when a Republican front-runner like Romney has been called a liar at least three times in a party debate? When Reagan ran in 1980, he and George H.W. Bush clashed hard over issues, but it was never personal -- and when it was over, Reagan tapped Bush as his running mate. Can anyone imagine Romney tapping Perry? If there is still a Republican establishment, its members ought to call the candidates and tell them to cool it. Call No. 1 should go to Santorum: For a man so far down in the polls to continue launching personal attacks against the party front-runner is both egotistical and self-indulgent.
All in all, another strong night for Mitt Romney. But those chuckles you hear are coming from Obama headquarters.
The opinions expressed in this commentary are solely those of David Gergen.