A group of hunger strikers known as the “Frisco Five” has captured the attention of City Hall, even prompting a failed visit from the mayor Monday.

But many elected officials who support the hunger strikers don’t believe Chief Greg Suhr should be fired or resign — a demand of the protesters. The chief’s absence, city leaders say, wouldn’t solve the department’s problems anyway.

Mayor Ed Lee’s impromptu Monday visit was rebuffed by the five hunger strikers, who for nearly two weeks have been camped outside of Mission Police Station in their efforts to pressure the firing of The City’s police chief following recent police killings and racist scandals in the ranks.

Lee reportedly entered the backdoor of the station and his staff informed the hunger strikers that the mayor would sit down with them inside the station. But the hunger strikers refused to participate in what they called an “ambush visit” and instead hollered their demands at Lee, who left after about a half hour.

“Mayor Lee went down to the Mission station to meet with the activists without conditions and they refused,” Lee’s spokesperson Christine Falvey wrote in a text message to the San Francisco Examiner. “He waited 30 minutes to give them a chance to change their minds and they still refused.”

The five hunger strikers, meanwhile, have their own so-called meeting at City Hall where they plan to march Tuesday afternoon and demand a meeting with the mayor after 13 days of fasting.

The march on City Hall is seemingly a perfect metaphor of the sometimes testy relationship between activists and their natural allies in City Hall. Many progressive lawmakers oppose the firing of Suhr, saying one man’s job will not help foment the systemic police reforms they are calling for following repeated police shootings and scandals.

Still, these legislators say the group’s pressure is working, as seen by the mayor’s visit Monday.

Supervisor John Avalos noted that there is often a nexus between the pressure street activism exerts on reform in local government.

“They are creating space for people like me to step in to make sure that City Hall is responding in some way,” said Avalos. “City Hall’s not gonna act on its own. It’s gonna be pressure from the outside…to drive change.”

Supervisor Eric Mar pointed out that often activists want more than politicians can deliver.

“There is always that disconnect where the demands are much more radical than the effort that comes from those of us inside City Hall,” said Eric Mar of the hunger strikers, who he supports.

Lee, who has directed Suhr and the Police Commission to reform the department’s use of force rules in an effort to reduce the number of fatal police shootings, has said he supports Suhr. Suhr has repeatedly stated he has no plans to retire.

Another local lawmaker said the real issue isn’t about one man but the department as a whole.

“The systemic change [that] needs to happen is bigger than one person,” said Supervisor Aaron Peskin. “It goes way beyond the chief.”

Mar agreed, voicing his tacit support for Suhr. “I think Chief Suhr is trying to address the systemic racism and bigotry in his department.”

But one of the hunger strikers, Ilyich Sato, aka Equipto, said while firing one man won’t solve the department’s issues, it will send a message the next chief would not be able to ignore.

For much of the last six months, activists have made it hard for local politicians to ignore their demands, even if the politicians have yet to meet them.

Since the December killing of Mario Woods by police, protesters have camped outside of Lee’s and Suhr’s houses, marched on City Hall, interrupted Lee’s inauguration and called an ongoing federal review of police a smokescreen.

The hunger strike is only the latest, and most serious, action taken in what appears to be a movement that has no signs of disappearing. On Monday, several of the “Frisco Five” signed paperwork known as an advance directive, which states they do not want to be force fed if they are hospitalized.

When asked how far she is willing to take the hunger strike, 66-year-old Maria Cristina Gutierrez said, “To the end.”

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