In a few hours of door-knocking, D.C. mayoral candidate Muriel Bowser is asked to prevent juvenile offenders from enjoying their incarceration, find a Metro job for a man who hasn’t applied for one and keep the cats off Maurice Ramsey’s porch.

Canvassing on the city council member’s home turf in Ward 4’s Brightwood and Petworth neighborhoods both requires and offers a pretty good sense of this corner of the city, where property values are rising, as is anxiety among longtime residents struggling to stay in their 1920s rowhouses alongside the newcomers with young families who’ve moved in and renovated. “Don’t you sell,’’ Bowser tells longtime district emergency medical technician Claudia Hudson, who says she has been on disability since the night eight years ago when she tried to lift a 600-pound patient, who was in a diabetic coma, onto a stretcher. “You’re responsible now,’’ she tells a man whose 87-year-old father has just died, leaving his son with a big property tax bill.

But an afternoon on the stump with her also showed that what some of us expect from local government, no six elves could deliver. And while there is some “I hear you,” and “We’ll keep an eye on that,” from Bowser — one of the eight Democrats running to replace scandal-encumbered incumbent Vincent C. Gray — what’s striking is how often she tells voters “No.”

As in no, she can’t get a parking ticket thrown out. No, “there’s not just a pot of money sitting there” for a concussion- awareness program. And no, she won’t commiserate with two men who think the mothers of their children have it made, raking in those assistance checks. “Personal responsibility cuts both ways,’’ she tells them.

The 41-year-old Bowser, who worked for Montgomery County before getting into politics, has long since learned that when it comes to her older constituents, she has to ask them if they need anything, because most of them would never ask her, or anybody. “There is so much isolation. I remember one man whose wife had just died bursting into tears,” she says, just because someone had asked him how he was doing.

Half a dozen aides fan out ahead of her, finding out who is home in the middle of the afternoon and preparing the way. “Right here!’’ they call, and Bowser bounds up the couple of short flights of stairs, calling, “Hel-LO!”

“Here’s the deal,’’ she tells them. “We want a fresh start at City Hall. Do you think we deserve that? Can I count on your support” on April 1? Or better yet, when early voting starts on March 17?

“Thank you for letting me represent you for the last seven years,’’ she tells an octogenarian who comes out on the porch in his stocking feet. The issue on his mind isn’t schools or ethics reform or public-private partnerships, but the neighbor who he says damaged the wall they share and then called him an ugly name. He’s already called her office about the beef yet doesn’t seem to expect her to do any more than listen and sympathize.

Which she does, pleasing him so much that he offers up an idea:

“You should run for mayor,’’ he tells her then, and she laughs and says yeah, she thinks so, too.

The next man on the block, though, expected action a while ago. “I’ve been calling your office for a year, and they won’t do anything,” Maurice Ramsey says angrily. That is, about the “hundreds of cats” he says a neighbor feeds — and that then befoul his lawn and porch. Though none seems to be around at the moment, they know when the cat daddy is about to appear and come running. Is there a mental-health issue with the neighbor, Bowser wants to know? Or a public-health issue? Well, no and not exactly: “He just feeds the cats.’’ Maybe, Bowser says, “we’ll see if animal control can come up with a plan.”

Canvassing “goes a little faster in the other wards,” she tells me as we walk away, “because these are my constituents now, and they need help now.”

They certainly remember everything she’s ever done for them: “She came out years ago when I did a cleanup campaign,’’ says Dee Taylor-Jolley, who takes a yard sign. But also what she didn’t do.

“I needed her very badly to get involved with a situation” with D.C.’s Department on Disability Services, says Keith Jarrell, and she did not.

Bowser has won the only two straw polls taken so far and is second in fund-raising only to longtime council member Jack Evans. Gray is third, having started late. So like others, Jarrell has come to see Bowser as the most plausible alternative to Gray.

Though he worked for Gray’s election, Jarrell said, “now I wouldn’t walk to the corner to shake his hand.” He has a sign in his yard for Ward 6 council member Tommy Wells, someone Jarrell has known “more years than I care to admit, but he isn’t going to get elected.’’ So he takes a sign from Bowser, too.

He thinks she’s “very personable,” he says, “very smart. . . . And when she’s mayor, we won’t have 500 families in hotels in Maryland,’’ he adds, referring to a recent Washington Post report that on any given night in the District, more than 4,200 people sleep in emergency homeless shelters, including more than 700 families staying in an abandoned hospital and overflow motel rooms. But, Jarrell says pointedly, “you don’t let people fall through the cracks.”

“And now,’’ Bowser says as we walk away from the decidedly mixed review, “you know that we didn’t rig the knock.”

On the contrary, the fluidity of the race is on full display, with a number of voters not yet firmly decided. “I’m not on your team; you never called me!’’ a retired teacher tells her. “I’m calling you now!’’ she returns, to his apparent satisfaction, since he then offers to host a fundraiser.

But to say that voters are unhappy with Gray would be playing down the sense of betrayal many say they feel. Retired corrections worker Gail Lyons says her only real starting point this election season is “that I sure wasn’t going to put Gray back in that seat.”

And Bowser’s onetime mentor, Adrian Fenty, who is going to be fundraising for her in Silicon Valley, seems to be looking better and better in the rear-view mirror: “I always said Fenty was arrogant,’’ Lyons added, “but he had a good head on his shoulders.’’

Like him, Bowser brags about having a base that cuts across racial lines, and she talks about how the divide in D.C. isn’t so much racial as generational and socioeconomic. On a long list of issues, she talks about striking a balance between old Washington and new, but is, she promises, a threat to the culture of corruption in the city where, as she tells everyone she sees, her family goes back five generations.

Her challenges now include winning over the older Washingtonians — black women in particular — with whom she lags in polling. Another hurdle is resisting the urge to make faces during debates — a temptation she tries to stave off by scribbling on a sheet of paper. The biggest surprise of the campaign, she says, has been all the free advice on the fashion makeover she didn’t know she needed.

Near the end of her walk, she gets only the second question of the day that doesn’t have to do with a voter’s own personal needs or agenda: “What are you going to do for the kids?” And in a dining room adorned with a large framed portrait of President Obama and first lady Michelle Obama, Bowser finally gets to deliver her well-honed spiel about improving middle schools and expanding training and summer programs to Olive Hudson and her son DeVon.

The most personal issue of all, though, may be this one, the one the election will turn on, though it isn’t yet clear how: Gray “came and talked to me personally and convinced me to vote for him,’’ said a still-smarting DeVon Hudson. “Then all this stuff came out” that made him regret that decision, even as the city did well.

His mother notes that she was living here before Bowser was born. “I’m 41,” the candidate protests, “so not a baby.” Hudson assures Bowser that she meant her words as a tribute to how much the councilwoman has done already. “I’m proud of you,’’ she says, and pulls her into a maternal hug.