Connolly pressing his early advantage

Connolly won more votes in the September preliminary than anyone else in the City Council race. He has raised - and spent - three times more money than his closest rival in the eight-way race for four at-large seats.

And he has an infant son, born the day before the preliminary election, as well as an 18-month-old daughter, leaving the candidate with heavy eyelids as he bounces from luncheons to candidate forums.

But Connolly, 36, has barely pulled back, leading many political observers to suggest that the lawyer and former teacher may have his sights on a higher office.

“The race for mayor begins Nov. 3 at 8:05 p.m. for John Connolly and a lot of others,’’ said Michael McCormack, a former city councilor and longtime political observer.

Of course, there have been plenty of previous promising council newcomers whose political careers have gone nowhere.

“I topped the ticket once,’’ said Lawrence S. DiCara, a former City Council president. “When I ran for mayor four years later, I came in a respectable fourth.’’

Connolly, though clearly ambitious, dismisses the talk about his future as meaningless political chatter, acknowledging that he benefited in September from having his name appear first on the preliminary election ballot. He will have no such luck next week, when his name will be sixth on the ballot.

“Every now and then, people come up and say something to me since I topped the ticket,’’ Connolly said. “Nobody ever said this to me before September.’’

The motivation that lights a fire in his belly - and leaves a knot of anxiety in his gullet - is the painful lesson he learned in his first race, when he faded in November after a strong finish in the preliminary.

“I just sit and think about waking up in 2005 in fifth place after everybody told me I was going to be the next city councilor,’’ he said. “And so, I try not to pay attention to any of that stuff.’’

The only other incumbent in the at-large race is Stephen J. Murphy, 52, a law-and-order councilor from Hyde Park first elected in 1997. Murphy and Connolly have had a sometimes bitter rivalry that boiled over in 2007 when Connolly acknowledged that his campaign mailed anonymous fliers suggesting that Murphy has been shopping for another job.

Connolly apologized and now says the flier was the “biggest mistake I’ve made’’ as a politician. Murphy, who finished 4,817 votes behind Connolly in the preliminary election, and who harbors his own mayoral aspirations, declined to speak on the record for this story.

Connolly hails from central casting of Massachusetts politics. His father, Michael J., was secretary of state for 16 years and serves on the Boston Licensing Board. His mother, Lynda M., is chief justice for the state’s district courts. John Connolly’s résumé boasts Roxbury Latin, Harvard College, Boston College Law, two stints as a teacher, and a partnership in a small law firm, which he balances with his City Council post.

The thumbnail biography in Connolly’s stump speech focuses largely on the three years he spent in middle-school classrooms, first at the Nativity Mission Center on the Lower East Side of Manhattan and then at Renaissance Charter Public School in Boston’s theater district. He touts education as his top priority and has pushed for an environmental sciences academy to prepare students for jobs in the green economy. He also proposes that the families of truant children be required to appear in court.

Connolly tells voters that he carries his classroom experience with him each day to City Hall, a refrain he repeated recently at the Twelfth Baptist Church in Roxbury, at a fried-chicken and green-bean lunch his campaign held for two dozen African-American veterans.

“I’m impressed by his presentation,’’ said Quaco Cloutterbuck, 73, who recognized Connolly from his previous visits to the veterans group. “He’s a father. He went to Harvard College, so he’s got to be bright. And he’s a hard worker.’’

Connolly is raising money at a pace without parallel in this year’s at-large race. Earlier this month, 150 people packed a Louisburg Square mansion, standing in a room with a soaring ceiling and museum-quality art, for a Connolly event.

Connolly fidgeted beneath a crystal chandelier, waiting for the applause to subside, before profusely thanking his hosts, Hilary and Christopher Gabrieli. Chris Gabrieli is a wealthy Democrat and former gubernatorial candidate, who acknowledged later that many in his home that night did not typically attend campaign events for City Council races. But the crowd, dominated by moneyed Beacon Hill neighbors and educators from local charter schools, showed up in force, sipping Chablis and Heineken as the youngest member of the City Council began his pitch.

“Would he be somebody I would support for mayor or some state office?’’ Gabrieli asked. “Absolutely.’’

Colleagues on the City Council describe Connolly as an eager and likable rookie who has carved a green niche for himself as chairman of the Environment and Health committee. Among his most tangible accomplishments, Connolly says, is working with the Menino administration to triple the number of hybrid vehicles that will be purchased by the city. The acquisition of the vehicles has been slowed, however, by the recession.

“I see him sometimes and he looks like he’s gone through a 13-round fight,’’ said John M. Tobin, a district councilor from West Roxbury who worked with Connolly as a young man hawking popcorn and soda at Fenway Park. “But I assume he going to top the ticket again and he’s leaving nothing to chance: what he’s done, the way he raises money. Put him on the list for a wide variety of things.’’

Andrew Ryan can be reached at aryan@globe.com.