Before Councilor Tito Jackson sat for a shave and trim, his South End barbers insisted that he do a few jumping jacks, biceps curls, and push-ups.

Jackson’s barbers figured he needed an edge — needed to get his “sexy back,’’ they said — as he spent a day campaigning in the biggest race of his political career.

Jackson is the underdog in his bid to unseat Mayor Martin J. Walsh; no challenger has beaten a sitting mayor in Boston since 1949. But his odds have seemed even longer in recent weeks as Walsh has found a national stage as a progressive big-city mayor opposing President Trump.

Undeterred by pundits counting him out, Jackson, a 41-year-old Grove Hall resident, exudes confidence. “We are going to win,’’ he said.

As he crisscrosses the city, he says he is running to give voice to people who feel left behind and ignored amid Boston’s building boom. He has found an audience in residents who have been displaced amid soaring rents, families trying to stay afloat, and parents in need of a champion for public schools.

Jackson and Walsh travel in the same ideological circles — both lean center left. Both support protections for immigrants, back women’s rights, and are strong advocates for the city. But they have different approaches to addressing the city’s nagging income inequality and fixing its public schools.

Jackson said he supports fully funding city schools to meet budget shortfalls and restore cuts. The mayor’s office said Walsh has pushed for reforms in the school system and has invested $143 million in increased funding to the district since taking office. To close the income inequality gap, both Jackson and the mayor would back investment in affordable housing and small businesses. Jackson has argued the city is not doing enough on either front.

Both oppose Trump’s policies. But Walsh’s public stance against the president’s threats to cut federal funding to Boston and other so-called sanctuary cities has exposed potential vulnerabilities for Jackson, said Erin O’Brien, political science department chairwoman at the University of Massachusetts Boston.

“Mayor Walsh has been recognized for finding his progressive mojo’’ after the presidential election, said O’Brien, who served as lead policy consultant with Walsh’s mayoral campaign. “It does make Tito Jackson’s job harder than it was a month and a half ago.’’

Darnell Williams, who heads the local Urban League, said black candidates seeking higher office often find themselves on “steep terrain’’ but added Jackson has time on his side.

“You can’t count a person out who is running and trying to win,’’ he said. “It’s a lifetime between now and November, and anything can happen.’’

Indeed, Walsh is not entirely problem-free. A cloud looms over his administration after two of his top aides were indicted in an ongoing federal corruption investigation.

Jackson, meanwhile, seems aware of his underdog status. With just $78,000 in the bank, he remains upbeat and steadfast. He vows to stay on message and build a grass-roots organization by focusing on residents in the city.

“The mayorship is not just about one person. It’s about the people,’’ Jackson said, pausing at a campaign party at Chez-Vous Skating Rink in Mattapan one evening. “We are campaigning across the city. And we are receiving a warm reception in all of the neighborhoods.’’

Jackson’s message resonates with Heather Cook, a South End mother of two. She said that since taking office, Walsh — who had supported a helipad for General Electric and is championed by labor unions — appears to be out of touch with people like her. City officials said the helipad would be state funded.

And what about Jackson’s prospects?

“It depends on who you ask,’’ Cook said. “If you ask the corporations who they support, they will say Mayor Walsh. But if you ask the residents around here, they will have a different view. [Jackson] is up for the challenge.’’

Boston’s mayoral races have long crushed challengers’ hopes. Councilor Michael Flaherty recalled his struggles as the last political underdog in Boston who tried to topple a sitting mayor — Thomas M. Menino — in 2009. Flaherty had name recognition and more than $2 million in campaign funds. His polling showed that Boston had grown younger and was eager for new leadership.

Still, he was no match for Menino and his political machine.

As he was talking to a potential voter one day, Flaherty recalled, a bus stopped in front of them with a giant picture of Menino hugging Red Sox slugger David “Big Papi’’ Ortiz.

“It’s a constant game,’’ Flaherty said. “You’ve got to stay in the mix and you scratch and claw for whatever attention you can get. The mayor is the star . . . but you are just trying to get some oxygen and start to come up with your own ideas.’’

Jackson contends Walsh has a three-year head start. So Jackson is focusing on what he sees as urgent issues across the city: In South Boston, Jackson said, people are dismayed by the massive tax incentives that attracted General Electric to the city. East Boston residents are worried about crime. In Roxbury, the fear is gentrification. Residents citywide want more jobs and better schools, he added.

He took his message to West Roxbury one morning as he shook hands with early risers at a Dunkin’ Donuts.

“I’m Tito Jackson, and I’m running for mayor,’’ he told them.

Some patrons hugged him, wished him well, encouraged him to take on Walsh.

“I need you,’’ he responded.

He persuaded James Ennis — a UPS diesel technician from Roslindale who had not been paying attention to the race — to hang Jackson campaign signs in his yard.

“I’d rather vote for him,’’ Ennis said.

At Chez-Vous in Mattapan, Evan Knight, a social worker, said Jackson just needs to keep being himself.

“When there is a sitting elected official, it’s always going to be an uphill battle for any challenger,’’ Knight reasoned. “But that doesn’t mean [winning] can’t be done.’’

It was a busy week for Jackson, who is chairman of the City Council’s Education Committee. At a School Committee budget hearing, he delivered what some called “The Tito Special,’’ a blistering critique of Walsh’s school spending plan.

“This budget is a dereliction of duty by our mayor,’’ Jackson said, urging a fully funded school system. He put the microphone back on the stand, and it dropped to the floor.

At City Hall, he demanded that protesters be allowed to enter the building to stage a second overnight sit-in outside the mayor’s office. He called for schools to offer sanctuary to immigrants. He railed against the lack of affordable housing at a Roxbury development project.

In the South End, the barbers at Top Notch barbershop peppered Jackson with questions, as Everard Bentley gave the councilor a lineup, trim, and dye for the grays sprinkled in his hair.

“People are struggling,’’ said Rally Hall, a barber who was incensed by the up to $25 million property-tax relief the city offered General Electric. “It doesn’t make any sense.’’

City officials stressed that incentive is contingent on GE adding 800 jobs. The city is expecting $60 million in tax revenue as a result of the deal.

The conversation ranged from crime to poverty to who is making the most 911 calls, but it came back to the plight of the middle class.

Cleon James, the owner, recalled how hard he and his neighbors worked to help clear crime from streets in his neighborhood. Now, people wonder if they will be able to stay.

“The community is safe now. Rent is going up now. It’s attractive now,’’ James said. “People have been here through the turmoil. Why raise the prices and kick them out?’’

Jackson listened intently.

“You better work on that, Tito,’’ James said.

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