Those skills have won him national attention and allowed him to recover from what he refers to as "the mistake that looms over all others": the self-inflicted humiliation two years ago of an affair with a television news anchor that ended his 20-year marriage and damaged his standing with many voters.
But he has not silenced doubts about his ability to follow through when the excitement subsides and the TV cameras are gone. For instance, Villaraigosa has boasted for years of his promise to plant 1 million trees across Los Angeles, calling it a cornerstone of his environment agenda. Yet only 200,000 trees have made it into the ground.
After four years, Villaraigosa says he has laid a foundation to alleviate traffic, create jobs and turn L.A. into the greenest big city in America, but his detractors -- and even some influential supporters -- still wonder if he can match his ability to campaign with a sustained effort to complete a major project.
That concern is heightened by Villaraigosa's flirtation with yet another campaign -- this time for governor in 2010. He offers no guarantee that if elected he would complete a second term as mayor.
'We were bold'
Villaraigosa's political achievements are substantial. Crime is down and hundreds of new police officers patrol the streets. And last fall, he helped win passage of a half-percentage point sales tax that will generate billions of dollars for mass transit projects, including the Subway to the Sea that he promised in his 2005 campaign.
"If you were to say to anybody that we would have passed a half-penny sales tax in the middle of a recession with a two-thirds vote, with opposition from across the county, most people would have said you were crazy," Villaraigosa said in a recent interview. "We weren't crazy, we were bold."
Early in his term, he failed to bring the Los Angeles Unified School District under his control. But then he rebounded with an orchestrated political coup: He tapped an array of companies that do business with City Hall to raise a record $3.5 million and get three favored candidates elected to the board so he would control the majority. In December, that majority replaced the superintendent with Villaraigosa's deputy mayor for education.
Villaraigosa has gained enough influence over the board that he says voters should "absolutely" hold him responsible for reforming the schools.
And he has enacted policies to rid L.A.'s port of smog-belching trucks and replace the city's controversial anti-gang program.
But the ultimate payoffs for those political victories -- less traffic, better-performing schools, cleaner air and fewer street gangs -- are still years away at best. Under current plans, the subway would not reach Westwood until 2032. By then, the 56-year-old mayor would be 79 and long out of office.
One measure of Villaraigosa's political strength is that city figures voice doubts about him in private. Few are willing to criticize him publicly.
Eli Broad, the billionaire philanthropist and civic activist, couches a criticism in a half-compliment, urging Villaraigosa to set aside aspirations for higher office and focus on his work in Los Angeles.
"I think he can become a great mayor. He has it in him. I sure hope so," he said.
During an interview in his spacious third-floor City Hall office, Villaraigosa acknowledged that many of his far-reaching promises, such as making Los Angeles the greenest big city in America and fixing a school district with 50% dropout rates at many high schools, will take more time.
"I asked the city to dream with me, and I've been bold," Villaraigosa said. "We have focused our efforts to build a foundation . . . and made a lot of progress."
He dismissed any suggestion of underachievement, reciting a list of accomplishments that he said already have made Los Angeles a better place to live. Among them: a 24% drop in violent crime; traffic improvements that include more left-turn signals and 1 million repaired potholes; the expansion of city after-school programs; and the construction of 1,044 housing units for the homeless.