With his resounding comeback win in Florida Tuesday, what have we learned about Mitt Romney? He can take a punch. He's shown the discipline, tenacity and organization to dismantle a vulnerable opponent. What we still don't know is whether the one-time, and now once again, GOP front-runner can make a convincing case for his own candidacy.

The Florida Republican primary race was a thing of beauty only if you like the Ultimate Fighting Championship on cable. Knocked back after his South Carolina defeat, Mr. Romney and his team came out swinging, kicking and clawing at Newt Gingrich. He delivered the blows himself and without apology in debates, and he unleashed his attack ads and surrogates to do the rest of the dirty work.

Mitt Romney after Tuesday night's primary in Tampa, Fla. Getty Images

While voters often claim to want a high-toned political debate, the reality is that they respond to critical information that goes unanswered. Republicans also want a standard-bearer who looks like he can survive the inevitable cage match with President Obama. That willingness to fight for conservative values was part of Mr. Gingrich's appeal in South Carolina, and in Florida Mr. Romney showed he'll do more than turn the other cheek.

Mr. Romney's cause was helped because the former House Speaker lacked the money to fight back in television ads and sometimes lacked a good answer because the charges were true. Mr. Romney's attacks on the Speaker's Congressional ethics were unfair. But it's hard for Mr. Gingrich to defend his $1.6 million contract with Freddie Mac, for example, at the same time he claims to be an outsider who would shake up Washington. Freddie Mac is the ultimate Beltway machine, and if Mr. Gingrich loses the nomination, one reason will be his decision to defend his Freddie contract by saying he was merely consulting as "an historian."

Mr. Gingrich also did not help himself with some of his own campaign arguments. In his fury against Mr. Romney, the speaker fired away in scattershot populist fashion, denouncing Wall Street, Goldman Sachs and other capitalist institutions in terms not all that different from Mr. Obama's.

This didn't help the credibility of Mr. Gingrich's theme that the race is between a "Reagan conservative and a Massachusetts moderate." Mr. Gingrich's tax plan is better than Mr. Romney's, but voters in Florida can be forgiven for not knowing it. The Speaker preferred to campaign against Bain Capital.

According to the exit polls, Mr. Gingrich lost overwhelmingly among voters who said the economy was the dominant issue, and he even lost to Mr. Romney as the candidate who voters said most identified with their concerns. When Mitt Romney outduels you as the man with the common touch, you have a larger problem than negative TV ads. Mr. Gingrich would do better to return to the more positive vision and activist agenda he laid out in his remarks Tuesday night.

Mr. Gingrich is vowing to fight on, and having already been counted out twice he has standing to do so. He won't have Mr. Romney's resources, but then with so many more states in play on Super Tuesday on March 6, Mr. Romney also won't be able to spend as much everywhere. The GOP has followed the Democratic Party's lead in allocating delegates on a proportional basis in most states, so Mr. Romney will need many more primaries to gather a majority.

As for the front-runner, his task now is to inspire a larger and more loyal following among Republicans and independents. One troubling sign is that nearly 40% of voters in Florida's exit poll said they would prefer that another candidate enter the race. Mr. Romney's largely negative campaign was able to demolish Mr. Gingrich, but it is also hurting his own favorability, especially among independents.

In his victory remarks Tuesday, Mr. Romney asserted that his party will unite behind his vision as a self-made businessman who can create jobs. He also laid out the distressing facts about Mr. Obama's economic record. (See editorial below.) Neither will be enough in November.

Every successful Presidential candidate needs two narratives that work together. One is personal, a biography that builds trust among voters and explains why he is up to the job. Mr. Romney has done this well, perhaps too well, because he seems to believe that his biography is his main selling point.

The other essential narrative is built around ideas that capture the national mood and offer a path to a better future. On this, Mr. Romney has far to go. His remarks in Tampa provided the outlines of a case against Mr. Obama, but they offered little to suggest how Mr. Romney would improve life for anxious Americans. They will not follow him merely because he saved the Olympics or ran a private-equity firm.

Successful U.S. candidates for the White House have understood that their mission is larger than their own ambition. It's about a cause, about "we" not "I." If Mr. Romney really wants to unite his party and rally a new American majority, he needs a cause bigger than his business biography.