Bostonians go to the polls Tuesday to reshape the City Council, the 13-member body that can hassle or boost Mayor Marty Walsh's City Hall agenda.

Voters could even give walking papers to two veteran pols in both citywide and district elections.

But in a sign that there's little enthusiasm from candidates as well as voters, there's only one challenger gunning for one of the city-spanning at-large seats. Annissa Essaibi George came in fifth place, just out of the money, in the council race two years ago. She's at it again, challenging councilors Michael Flaherty, Michelle Wu, Stephen Murphy and Ayanna Pressley.

Of the four incumbents, it's Murphy who most City Hall-watchers agree is the most vulnerable to George. The Hyde Park veteran has built a reputation for old-school politicking that's kept his constituents happy term after term, but recent squabbles over the council's salary may have damaged Murphy's appeal.

"Steve Murphy has been written off since I had a full head of hair and he always survives," lawyer and former City Councilor Larry DiCara told WGBH News. "And he survives because he has very strong support in Hyde Park, Roslindale, West Roxbury, other high-voting districts."

The most shocking development from September's preliminary election, which settled the field for Tuesday's action, came in District 4, where incumbent councilor Charles Yancey came in second to newcomer Andrea Campbell.

Yancey hasn't been on the council for over 30 years without a solid voter block putting him back in office year after year, but he'll have to push his supporters in Mattapan and Dorchester harder than he ever has to overcome Campbell's extremely well-funded campaign.

"This is a real fight," DiCara said. "I expect it to be a five or 10 percent fight. I don't think it's a landslide on either side, but this is a real battle."

DiCara described the District 4 race as "one of generation and one of personality," with Campbell, 33, giving Yancey, 67, the challenge of his career.

"He has more lives that the proverbial cat," DiCara said. "He has a challenger who is exciting people, who is getting people out to work on her behalf, raising a lot of money."

On the at-large side, DiCara suspects Murphy, while vulnerable, will come in fourth place to keep his seat when the dust settles.

DiCara expects turnout in the city to be low, even for an off-year election, somewhere in the range of 40,000 to 45,000 voters.

Who will show — either out of habit or because of motivated campaigns — up is what will make the difference.

"Low turnouts tend to be older, tend to be made up of people in the traditional wards where people own single- and two- or three-family homes as opposed to people who rent," DiCara said.

And that, DiCara says, means that when voters are set in their ways, incumbents have the advantage.

So who does vote in this kind of obscure off-off-year election?

"In general, the people who vote are high-frequency voters, tend to be more educated, tend to be political 'in-the-know' folks," said Pam Wilmot, executive director of Common Cause, a Massachusetts-based government accountability and transparency advocacy group.

"What we really need government to do is to represent everyone, especially the disenfranchised," Wilmot said. "And they're exactly the ones who won't be voting in this election, or frankly, in very many elections."

Wilmot thinks it's time for the state to think about moving its off-year municipal elections to fall the same day as voting for more popular offices like governor and president.

"There's just too much voter fatigue," she said. "There's too many things to pay attention to and you essentially have the outcome of a very important race that may have a significant impact on City Council decided by a very, very low percentage of voters."

The bad news for George continues, since she's built one of her voter bases in East Boston, where she is a public school teacher. Turnout in that neighborhood isn't expected to go through the roof, which could hurt her.

The makeup of the council matters, especially to Mayor Marty Walsh, whose policies get vetted by the 13-member panel.

"These races don't get much attention, but they do matter," former councilor and mayoral candidate John Connolly told WGBH News. "If one or two seats change hands, that can totally reshape the race to be the next council president in January. It also matters for the mayor, in that it is much easier to move your agenda with a more friendly council president,"

DiCara's been watching City Hall politics as long as anyone, having been first elected to the council himself in 1972. That year, DiCara said, there were 41 challengers for a mere nine seats in the panel.

"That's a barometer of the diminished importance of local politics to increasing proportions of the electorate," DiCara said.