Debates about how best to handle crime, mental health and homelessness come as the pandemic exacerbates many of those longstanding issues around the country.“The underlying conditions were never addressed, so we’re now at a moment where it feels like a powder keg is exploding,” said Donovan Richards, the Queens borough president. Describing how entrenched many of those overlapping problems are, he continued, “Eric ran on a platform of safety, and it’s going to be a challenge.”Lawmakers and Asian American community leaders said in interviews that the mayor has moved urgently behind the scenes to share information after the killing of Ms. Go. The police have said there is no indication that she was targeted because of her ethnicity, but the shoving was perhaps especially wrenching for many New Yorkers of Asian descent, a diverse constituency that has experienced soaring bias crimes amid the pandemic.On Saturday, Mr. Adams convened a Zoom meeting, inviting Asian American elected officials from across the city, elected leaders from Manhattan and community advocates, the mayor’s office said. The police commissioner, Keechant Sewell, and several chiefs also attended.“Whatever the charges are, our community is really reeling right now,” said Jo-Ann Yoo, the executive director of the Asian American Federation. “I just appreciated the fact that he reached out to even engage us that way.”The mayor also told State Senator John C. Liu about the Times Square killing before Mr. Liu had seen news accounts, and Mr. Liu said that Mr. Adams had “handled it better than anybody else has handled it in recent memory.” But the bar Mr. Adams must keep meeting, he suggested, is a high one.“Voters have considerably high expectations from Mayor Adams when it comes to public safety,” Mr. Liu said. “He made an issue out of it during the campaign, rightfully so, and people will expect him to deliver.”Mr. Adams said on Monday that he was keenly aware of that dynamic.“I want the expectations to be high,” he said. “The stakes are high.”