CHICAGO — (CNN) Andrea Zopp has every reason to call for embattled Chicago Mayor Rahm Emanuel to resign. The Senate Democratic candidate is seeking a leg-up in a contested primary at a time when Emanuel’s handling of police violence has enraged many in the city’s large population of African-American voters.

But Zopp is declining to call on Emanuel to step aside.

“I certainly understand the frustration of those who are calling for the mayor’s resignation and their view that he has not handled these issues well,” Zopp, a former head of the Chicago Urban League, told CNN on Monday. “My view is that he is there, and he is paying attention and we have his ear. We ought to use it to drive real change.”

Zopp is hardly alone. Protesters may be taking to the streets and demanding Emanuel’s resignation, but many in the Illinois political establishment are more resistant to join the fray. The state’s congressional delegation has stayed mum on Emanuel’s future, and many aldermen on the Chicago City Council — including in the black caucus — have yet to call on him to resign. A new bill in the state legislature in Springfield to let Chicago voters recall Emanuel has won only scant support and is opposed by powerful Democratic leaders.

In short, Emanuel seems safe — for now.

“I’m not suggesting that the mayor needs to resign,” Rep. Danny Davis, a 10-term congressmen and veteran of the Congressional Black Caucus, told CNN Monday. “I am suggesting that we need to overhaul in a very serious way the culture of law enforcement in our county.”

Davis’ voice carries extra significance since it was in his West Chicago district where the latest episode of police violence occurred over the weekend. After responding to a call of domestic violence, police shot and killed 55-year-old Bettie Jones, and 19-year-old Quintonio LeGrier, who appeared to be suffering from mental health issues. Police said that Jones — an African-American mother of five — had been “accidentally” shot.

The deadly incident occurred after Chicago garnered national attention following last month’s release of a 2014 video showing a white police officer firing 16 times at a black teenager, Laquan McDonald. Emanuel, under siege, fired Police Superintendent Garry McCarthy, called for a series of reforms, and said he “welcomed” the Justice Department investigating the practices of the Chicago police. He held meetings with numerous black Chicago leaders and showed a softer side rarely seen by the brash former chief of staff to Barack Obama.

“He’s called me a number of times” over the past month, Davis said. “The mayor is as engaged as comprehensively as he can be.”

Rep. Bobby Rush, a 12-term Chicago congressman and influential African-American voice in the city’s politics, said in a letter to the Chicago Sun-Times this month that ousting Emanuel would “only move from one chaos to another chaos,” calling it a “bad strategy.”

Despite the olive branch from political leaders, the backing is still tenuous. After struggling to win re-election earlier this year and being forced into a runoff, Emanuel has seen his poll numbers plummet. Chicago officials say that further missteps by the mayor could cause a revolt within the party establishment.

Howard Brookins, a Chicago alderman and former chairman of the city council’s black caucus, told CNN Monday he isn’t calling on Emanuel to resign but has “been disappointed in the handling of this matter” since April when he called for the release of the McDonald video.

With the uproar intensifying following the weekend’s shootings, the Chicago mayor announced Monday that he’d cut short his family vacation to Cuba and return to Chicago and deal with the aftermath Tuesday afternoon.

“The mayor is energized by the challenges facing the city, and he is committed to driving real and lasting solutions,” Stephen Spector, a spokesman for Emanuel, said when asked about calls for him to resign. “As part of that process, Mayor Emanuel is taking action to restore accountability and trust in the Chicago Police Department, and he will continue to actively engage residents and community leaders to ensure their voices are heard.”

A person familiar with Emanuel’s thinking said that the mayor felt like he could weather the storm, in no small part because his allies are keeping their powder dry and the loudest critics of the mayor are ones who backed his opponent in the 2015 mayoral race, Jesus “Chuy” Garcia. Moreover, critics lack any real mechanism to eject him from his position, and there is ample time to restore the mayor’s credibility before the 2019 elections, the mayor’s allies believe.

Still, Emanuel’s team is well aware that the calculus could change immediately if public pressure continues to mount. Some progressives continued to pound Emanuel in the aftermath of the weekend shooting.

“I don’t see how he can continue governing now,” Rev. Al Sharpton said on MSNBC’s “Morning Joe” Monday. “Now I think he’s going beyond the point where he can even govern with the trust of the people.”

Trying to seize on Emanuel’s vulnerability, state Rep. La Shawn Ford, a Democrat from Chicago, introduced a bill in the legislature to allow Chicago voters to recall the mayor from office.

“I think he wants to be held accountable, and that’s all this bill does,” Ford said in an interview Monday, predicting that support would grow in the new year.

But Ford has few allies in his fight so far. A spokesman for the powerful state House speaker, Michael Madigan, said the influential Democrat “doesn’t have a position” on the bill just yet. And Rikeesha Phelon, a spokesperson for John Cullerton, a Democrat who is the president of the state Senate, said the lawmaker believes the bill “establishes a dangerous path.”

Emanuel, a former Chicago congressman who has battled with the teacher’s unions since becoming mayor in 2011, has increasingly been viewed with disdain among elements of the left — especially in less affluent, black communities on Chicago’s South Side. And after the video release of McDonald’s shooting, national liberal activists delivered 250,000 signatures calling for the resignation of Emanuel and Cook County state’s attorney, Anita Alvarez.

But activists later told the local press that a small percentage of signatories were Chicago voters, a sign that the combative mayor has some breathing room to deal with his mounting problems.

Indeed, U.S. Rep. Tammy Duckworth, a candidate preferred by Washington Democrats for their party’s nomination for the state’s Senate seat next year, said Monday she isn’t seeking Emanuel’s ouster.

“Tammy believes the mayor has been saying the right things, but now it’s time to do the right things because without real change, words are meaningless,” said Matt McGrath, Duckworth’s campaign spokesman.

The-CNN-Wire ™ & © 2015 Cable News Network, Inc., a Time Warner Company. All rights reserved.