Two, sometimes three times a day, you can catch Hans Kolbe and Kirby, his poodle-terrier, strolling the sloping streets of Dolores Heights.

Bound for Dolores Park from Kolbe’s home on 21st Street, their jaunts almost inevitably lead them to the stately Sanchez Street stairs.

But with dispiriting predictability, navigating the staircase means hop-scotching over piles and puddles of human and canine waste — the stairs have become an open-air latrine.

When he’s not pressed for time, Kolbe tries to be diligent about snapping photos to report the messes to the city’s 311 customer service site. Cleaning crews have been fairly responsive, Kolbe said, but he’s baffled as to why the steps remain such a persistent problem.

“The frustrating thing is, this happens every day, twice a day. It’s not an unknown thing to the city,” Kolbe said. “How in the hell can we make sure our city services cover these kind of predictable issues in a predictable manner? It’s not rocket science. The frustration level that people feel is just incredible.”

Fed up with the unevenness of the city’s attentiveness, Kolbe and a group of residents in Dolores Heights, Eureka Valley, the Castro and other nearby neighborhoods have spent more than a year organizing what could become San Francisco’s second GBD (green benefit district) — a zone in which property owners pay a special assessment and hire private firms to provide services on top of the city’s.

But the proposal has kindled a backlash among some residents living inside the 90 blocks that comprise the proposed GBD. Most lament the same street-level problems as Kolbe, but balk at paying more in taxes to supplement basic services they believe the city should provide. Largely for those reasons, the long-standing Mission Dolores Neighborhood Association has come out against the project.

“We’re talking about paying a third party to organize and perform activities that the city should already be doing,” said Rick Carell, who lives in the district’s proposed boundaries. “How about we get the cops and Public Works to do their damn jobs?”

Carell and others opposed to the GBD also believe the city is subtly encouraging the district’s formation. The city has spent hundreds of thousands of dollars to facilitate the district’s formation — conducting community outreach and drafting legal documents — but officials say the city remains agnostic as to the ultimate outcome.

“Yes, the city should do more,” said Carolyn Thomas, who sits on the GBD’s steering committee, along with Kolbe. “But do you really want to wait 10 years for them to do it? And do you have much faith that they will?”

If they’re successful, about 4,300 property owners — both residents and businesses — would pay a special assessment every year to fund private services such as enhanced sidewalk cleaning, trash-removal, power-washing and landscape improvements. The district’s operating budget would be about $1.1 million in its first year — 86% would be spent on street cleaning and beautification efforts.

The money would also pay the salary of an executive director.

The genesis of the GBD was the weekend bacchanals that commenced after the reopening of Dolores Park in 2016 and a string of violent confrontations at the park last summer.

Then-District Eight Supervisor Jeff Sheehy set aside $200,000 for neighborhood improvements over two years. Around $70,000 was used for steam cleaning, mostly around the 18th Street commercial corridor, but residents wanted to find longer-term solutions that would be accountable to community interests. A GBD emerged as the way to do that.

At the request of residents, city officials shifted the remaining $130,000 to fund the formation process, which includes gauging whether there was enough community interest to create it. Most of that money has been funneled to the private San Francisco Parks Alliance to manage the process. The organization has spent just over $70,000 to date.

“Giving neighborhoods the tools they need to help themselves is deep in our DNA. From our perspective, the GBD is the ultimate ‘bottom-up’ method to beautify our shared spaces,” Parks Alliance CEO Drew Becher said in an email.

The average single-family home or condo owner would pay an extra $100 to $250 annually if the district is approved, based on a formula that factors in the square footage of each parcel’s lot and structures.

There’s also a proposed “enhanced service zone” along Valencia Street between Duboce Avenue and 22nd Street, where the assessment rate would be nearly double to pay for additional cleaning and beautification. The extra services came at the request of Valencia merchants and property owners, according to the Parks Alliance. The costs would be halved for nonprofits.

Overall, a larger property means a bigger tax bill, but it also means a larger, “weighted” vote in the two elections needed to create the GBD, the first of which is under way.

Petitions meant to gauge whether there’s a minimal level of support for the district have been sent out. If enough petitions come back in support of the GBD, the district’s organizers can petition the Board of Supervisors to launch the second election, which requires a simple-majority vote to approve creation of the district. If that threshold is met, the board would have to agree to add the assessment to property owners’ tax bills.

Largely because of Dolores Park, the San Francisco Recreation and Park Department would be the largest property owner in the proposed district and therefore would get the largest vote.

Rec and Park spokeswoman Tamara Aparton said the department will not vote in the first election. But if the second election takes place, the department will vote in favor of the GBD. The city would be on the hook for about $30,000 annually if the GBD moves forward, given the amount of property it owns within the district’s boundaries.

“We think it’s great when neighbors get together to support public spaces, and it’s important that any proposal enjoys broad community support before moving forward,” she said in an email.

That, according to critics of the proposal, is still evidence of the city putting its thumb on the scale of the formation process.

“You can feel the power and the presence and the money of the city trying to push this on us, and we’re trying to band together to fight it,” said Stephen Bartoletti, a resident of Corona Heights and a member of a loose coalition of residents, many of whom live outside of Mission Dolores, organizing a fight against the GBD and the GBD model in general.

The group opposes the spot-taxing of neighborhoods and the creation of tiered city services. Two proposed GBDs have foundered in recent years, in the Buena Vista area and Inner Sunset, thanks in part to organized opposition.

Only one GBD has been launched to date: the Dogpatch Northwest Potrero Hill Green Benefit District. Then-Supervisor Malia Cohen authored legislation in 2013 that allowed the city to create GBDs to lay the groundwork for the Dogpatch district.

“I share the concerns of people who feel government should be doing this and doing it effectively. But I want to hear a bit more of where it seems like folks in these neighborhoods are,” said Supervisor Rafael Mandelman, who represents the areas encompassed by the GBD.

“I’m reluctant to push too heavily for this funding structure without knowing there is real grassroots support for it,” he said. “If there seems like there’s significant support for formation, I may come out more strongly for one.”

Dominic Fracassa is a San Francisco Chronicle staff writer. Email: dfracassa@sfchronicle.com Twitter: @dominicfracassa