One of the best ways to grasp the roots of singer Gloria Estefan's popularity is to watch what happens when she stops for a cup of café cubano at an outdoor table in Miami's Little Havana, as she did one day last summer. "She makes me cry, she is so beautiful," said Linda Fernandez, one of dozens of fans who poured out of shops and restaurants to take a gander at the community's most famous alumna. "There is no one in the world who means as much to Cuban people," said another, perhaps hyperbolic, admirer, clutching an autograph. "When she sings, I cry. I am so proud of her."

Which helps explain why Miamians reacted as if to a family tragedy after Estefan, 32, suffered a broken back on March 20 when her tour bus was rammed by a semi truck near Tobyhanna, Pa. Early bulletins reported the singer in critical condition and possibly paralyzed for life. Her husband, Emilio, 37, their son, Nayib, 9, and three other passengers were also injured, but none as seriously as Estefan. Tour driver Ron "Bear" Jones says Estefan was asleep on a couch when the bus, which had come to a stop after a truck jack-knifed in the road ahead, was hit from behind by a second semi. The bus then plowed into the jackknifed vehicle, pitching Estefan violently to the floor. Says Nayib's tutor, Lori Rooney: "Gloria appeared to be in terrible pain. But her only concern was to make sure Nayib thought she was okay."

Fan and media response was immediate. Six South Florida TV stations dispatched reporters and crews to the crash site (one set up a 900 number to record get-well wishes), tearful fans gathered outside the band's business offices and some Miami deejays began playing Estefan's records nonstop. Even after doctors at Scranton's Community Medical Center announced that she was out of immediate danger and would not be paralyzed, the demand back home for news continued unabated. "I don't think we realized how popular Gloria was in Miami till this," says Dr. Steve Greenberg, medical reporter for Miami's WCIX-TV. The day before the accident, Estefan had met with President Bush to discuss joining the war on drugs. Said Miami Mayor Xavier Suarez, who can recall the days when Estefan played weddings and bar mitzvahs: "To see her at the White House made me proud. Seeing her in the hospital made us all a wreck."

He and his constituents weren't alone. Bruce Springsteen, Jon Bon Jovi, Dick Clark, Guns N' Roses, Billy Crystal and Madonna sent flowers; Prince and record mogul David Geffen sent CDs; and President Bush called—twice.

Estefan received that kind of response, says Clark, because she "is just a kind, down-to-earth, lovely lady." Echoes Miami-based talk show host Cristina Saralegui, a friend: "When you think of entertainers, most people envision an exotic life. But Gloria and Emilio have the most old-fashioned, square marriage. One day, long after Gloria made it big, she came over to take our kids to the beach. No maids, no helpers, just Gloria. She said, 'Look. I've got two hands to spank two little butts, so everybody better behave.' You better believe they listened to her. She's shown you don't have to give up the normal things, like a good husband and family, if you want success."

Strength of character is a trait that friends have come to recognize in the Cuban-born pop star. In her teens she helped nurse her father—an ex-Batista family bodyguard, Bay of Pigs invader and Vietnam vet—through multiple sclerosis. He died in 1980. Her mother, Gloria Fajardo, still teaches fifth grade in Miami. Estefan earned a B.A. in psychology from the University of Miami in 1978 and worked as a Customs interpreter—she speaks French too—while pursuing her musical career. In 1979 she married Emilio, founder of the Miami Sound Machine, the hot local band she sang with. The group scored a watershed crossover hit with the single "Conga" in 1985 and went on to sell 10 million LPs. They rechristened themselves Gloria Estefan and the Miami Sound Machine for their latest album, Cuts Both Ways.

According to Dr. Harry Schmaltz, who treated Estefan in Scranton, the singer came close to losing it all in the accident: "Another half inch of movement of the spine, she'd be completely paralyzed." Following successful surgery in New York City on March 22, Estefan was left with two metal rods implanted to brace her spine and a permanent, 14-inch scar left by the incision. "She's a wonderful patient," says operating surgeon Michael Neuwirth. "There is nothing prima donnaish about her at all."

Estefan faces six months of convalescence and painful therapy, but has already taken her first tentative steps. Friends and fans hope that—to paraphrase her best-known hit—recovering enough to do the conga will take Estefan only a little longa.

—Steve Dougherty, Alex Connock in Scranton and Deborah Wilker and Denise Stinson in Miami