The monotony of a City Council meeting gave way to a rare moment of discord recently, when Councilor Tito Jackson rose to excoriate the administration of Mayor Martin J. Walsh over what he described as its inconsistent tax policies.

He lambasted Walsh’s recent tax relief proposal, saying it would hurt the public school budget.

“I think sadly our tax collectors as well as the Walsh administration are not dealing with issues at hand,’’ said Jackson last week.

For much of the year, the suave politician from Roxbury has been a thorn in Walsh’s side over the school budget and the administration’s handling of crime, fueling speculation that Jackson might challenge the mayor next year. Jackson has told the Globe he is “strongly considering’’ a run, adding that he wants to unite the city, particularly since the presidential election.

The councilor, who has not officially declared his intentions, would face long odds if he did: His political war chest is 1 percent the size of Walsh’s coffers, and Jackson’s political machine and the number of his supporters are a fraction of the mayor’s.

Nor is history on his side: No incumbent Boston mayor has lost reelection in nearly 70 years.

Still, in recent months, Jackson has been sharpening his rhetoric against the mayor on the council floor, signaling his serious interest in the job, including getting help from a master political fund-raiser before a key year-end deadline.

Walsh, whose administration has been hit by two federal indictments, has repeatedly said that he’s not focused on any challengers — including Jackson — but he’s also emphasized that he is not taking his reelection for granted. He has been quietly campaigning, holding at least nine political events from East Boston to Roxbury, with a big launch expected next year.

“Tito is a friend,’’ Walsh said recently in response to a question about a possible Jackson challenge. “He supported me when I ran for mayor in 2013, and I would love to have his support in 2017.’’

Jackson, in a show of his growing confidence,hired Kentucky fund-raiser LA Harris & Associates LLC this fall to boost his campaign coffers, paying the company two installments totaling more than $5,000 since October, state records show.

The councilor also wooed donors at the swanky Mandarin Oriental Hotel in Back Bay last month, raising over $10,000 from supporters who propelled him to office during his first successful council run in 2011, according to a person close to Jackson’s campaign.

Jackson declined to say whether the event was for a potential mayoral run or his council reelection. Councilors are holding fund-raisers for their elections next year. State rules allow candidates to transfer funds to run for other offices.

“I have an election next year,’’ Jackson said when pressed on the issue. “I am the District 7 councilor.’’

He said he retained LA Harris to professionalize the fund-raising machine for the Committee to Elect Tito Jackson.

This is usually the time of year when elected officials signal to donors their intentions for reelection or a goal for a higher office, to maximize contributions this year and next. That was the case recently when Mayor Setti Warren of Newton announced he would not seek another term in office and began calling donors for a possible bid for governor in 2018. State law allows individuals to donate a maximum of $1,000 per year.

Jackson’s campaign account balance is $32,000, while the mayor has $3.3 million in the bank, according to state finance records and the mayor’s campaign.

As of yet, no one has publicly declared a challenge to the mayor. If Jackson decides to run, it could be tricky for Walsh, particularly in the black community, a voting bloc that eased Walsh to victory three years ago, some political watchers say.

“Walsh is not vulnerable to another white guy Democrat running,’’ said Erin O’Brien, political science chairwoman at the University of Massachusetts at Boston. She was also a lead policy consultant with Walsh’s mayoral campaign. “If there is anybody that would beat him, it’s a person of color that draws on different portions of the Democratic Party than Walsh does.’’

While the mayor is well liked in the city, O’Brien said, he has plenty of vulnerabilities a challenger could exploit. The contender could make issues out of the federal investigation looming over City Hall that led to the indictment of two Walsh staff members on extortion charges.

Other sources of contention include the failed Olympics and IndyCar race bids, plus a host of public education issues such as possible school closings, the public school budget, and the Boston Latin School crisis.

Both Walsh, the 49-year-old plain-spoken labor champion, and Jackson, the 41-year-old chairman of the council’s education committee, have compelling narratives of defeating the odds. Walsh was raised by Irish immigrants in a triple-decker. He overcame cancer, alcoholism, and being hit by a stray bullet — rising to lead the building trades union and become a state representative and now mayor.

Jackson captivated the council floor in 2014 when he shared the story of how he was born to a 13-year-old girl who had been sexually assaulted. He was adopted by Grove Hall activists, who supporters say taught him the value of fighting for the poor and uplifting his community.

“His mantra is standing up for the little guy against the system,’’ said Darnell Williams, a Roxbury resident and activist who knows Jackson well. “It’s in his DNA. It’s not a new thing for him. This is who he is.’’

Jackson graduated from the University of New Hampshire and worked in sales and marketing before joining the administration of former governor Deval Patrick. In 2010, he was political director for Patrick’s successful reelection. He ran for and lost an at-large City Council seat in 2009 but triumphed in 2011 in a special election to replace Chuck Turner, who was expelled from the council after he was convicted in a federal corruption case.

Walsh and Jackson were once allies. In the closing hours of the 2013 mayoral election, Jackson was among the elected leaders who stood elbow-to-elbow with Walsh over his challenger, former city councilor John Connolly. But in more recent months, Jackson, political experts say, has pushed Walsh to sharpen his stance on the charter school ballot initiative that Jackson opposed.

Now settling comfortably in the job as the city’s 54th mayor, Walsh has moved to solidify his public standing with efforts such as a citywide race dialogue, tax relief for Boston homeowners, and maintaining the city’s strong fiscal standing. He has made strengthening schools a mission, attracted General Electric to the city, and upgraded the city’s digital infrastructure.

Recently the mayor has been making the case for a second term at several campaign events, including in Jamaica Plain, South Boston, Mattapan, and the Bowdoin-Geneva section of Dorchester. He said he expects the campaign will pick up steam next year.

Meghan E. Irons can be reached at meghan.irons@globe.com. Follow her on Twitter @meghanirons.