MIAMI—Things ought to be pretty good for Jeb Bush right now. The former Florida governor leads by a narrow margin in national polls for the Republican presidential nomination, and by a wider margin in New Hampshire. He is overwhelmingly dominant in fundraising. And he does not lack for connections to the Republican donors, officials, and grandees collectively known as "the Establishment."

Yet before Bush's campaign could even officially begin on Monday, it seemed to be falling apart. His staff was in turmoil, the apparent result of tensions between new hires and longtime loyalists and potential opponents, unintimidated, kept jumping into the race. Bush's poll numbers, while still good enough for first place in a 15-way contest, have been on a downward trajectory since he stepped out on the campaign circuit. Pundits have compared him to Rudy Giuliani, the former New York mayor who led the field in the early run-up to the 2008 primaries, only to see his candidacy collapse when Republican activists in early-voting states turned their backs. The party that nurtured Bush's father and older brother seemed disinclined to grant him the same deference.

And so the stakes were high as Bush took the stage here on Monday, in a community-college gymnasium in a heavily Cuban neighborhood. The arena was packed with a diverse and passionate crowd (about 3,000, according to the campaign). They carried inflatable thundersticks and red-and-white signs with the candidate's exclamatory new logo, "Jeb!" (in Spanish: "¡Jeb!"). Bush was preceded onstage by a family of Cuban salsa musicians; an African American pastor; a Colombian American advocate for children with disabilities; his own Mexican American son, Texas Land Commissioner George P. Bush; and two slickly produced biographical videos. The ambiance, some noted, was that of a national convention in miniature, as if Bush could project his way to the nomination by acting as if he'd already achieved it.

Bush's speech maintained the ruse. He attacked not his Republican rivals but President Obama, Hillary Clinton, and "the progressive agenda." He promised 4 percent growth and 19 million new jobs, through a regimen of tax and spending cuts. He promised school choice, religious liberty, and a rebuilt military. He spoke a few sentences in fluent Spanish. "Not a one of us deserves the job by right of resume, party, seniority, family, or family narrative," he said. "It’s nobody’s turn. It’s everybody’s test, and it’s wide open."

Bush leaned hard on his Florida record, which his campaign has indicated will be the focus of his relaunched message. Education reform—a far-reaching expansion of vouchers, charter schools, and high-stakes testing, which critics say hollowed out the public education system with questionable results—was a centerpiece of his tenure. The economy grew, though largely on the back of a population and real-estate boom that would crash to a halt shortly after he left office. Bush enjoyed broad, robust popularity and a reputation for seriousness and determination. In the audience after the speech, I met a Democrat and environmentalist named Jenny May who said she passionately supported Bush since working with him on Everglades preservation. “He sits down at the table and he listens to everyone,” she said. “He walks the walk.”

As written, Bush's speech did not mention immigration. In the past few years, he has written a whole book advocating immigration reform and said that many undocumented immigrants are guilty only of “an act of love.” His position has left Bush in a difficult bind. In a general election, support for immigration reform is broadly popular, particularly with the Hispanic voters Republicans will need to win—but many committed GOP activists are adamantly against it. Activists on the other side of the debate, meanwhile, criticize Bush for not going far enough. Midway through Bush's speech, a row of spectators suddenly stood up and tore off their overshirts, revealing neon-yellow T-shirts underneath that spelled out “LEGAL STATUS IS NOT ENOUGH” one letter at a time.

The crowd tried to shout down the protesters (who, having made their point, filed out through a nearby door), but Bush took the bait: “The next president will pass meaningful immigration reform so that that will be solved—not by executive order,” he said. It was not exactly a commitment, and it was cloaked as an implicit attack on Obama. But it was a signal that Bush didn't intend to try to avoid the issue.

As a speaker, Bush is (like Hillary Clinton) workmanlike at best. Engaging, if intense, in one-on-one interactions, he often seems bored with the choreography of public speaking. Throughout Monday's address, he had a slightly panicked look in his eyes; pausing to let the crowd cheer, he clasped his hands in front of him and stepped away from the podium, looking around uncertainly. Clinton's kickoff speech on Saturday was mostly devoid of pageantry—there was, for example, no parade of introductory speakers—as if to strip away her larger-than-life aura and bring her down earth. Bush's presentation was the opposite, a campaign trying to build its man up and convince people he was bigger than he seemed.

What has gone wrong for Bush so far? Some have characterized it as a policy problem—the party has moved right since he was in office, from 1998 to 2006, and its activist base loathes the Common Core educational standards, which Bush championed, as well as immigration reform. Others have theorized that the problem was one of perception, pointing out that Bush racked up a slew of conservative accomplishments as governor—the party activists elsewhere just had not gotten the message. (“We're not talking about a health-care bill in Massachusetts,” former Senator Mel Martinez told me, an implicit jab at 2012 nominee Mitt Romney. “He had a very conservative record as governor. He ended affirmative action!”)

My own view is that Bush's problem has mainly been one of performance: He just hasn't impressed people since reemerging on the political scene. Republicans were open to the idea of him—in a CNN poll in December, when he first began exploring a run, he had the support of 23 percent. But as they watched him give mediocre speeches and fumble obvious questions—notably the one on Iraq, which took him days to get straight—their ardor dimmed and his standing dropped.

Republicans, who have lost the popular vote in five of the last six presidential elections, badly want to win this time around. Many of the activists I've spoken to—even staunch conservatives in rural Iowa—are concerned primarily with nominating a candidate who can win a general election; they are haunted by the unexpected defeat in 2012, and with it, a bewildering sense that they are out of sync with their country's mainstream. But Bush's stumbles—and their array of other options—make them wonder if he is the candidate who can turn the tide. Why compromise their beliefs for someone who can’t close the deal?

On Monday, Bush tried to impress them with a vision of the future with him as the nominee. In the coming months, he must convince them to believe in it.