CHICAGO — GQ, the men’s magazine, just named Mayor Rahm Emanuel to its list of “The Worst People of 2015.” In Springfield, the Illinois capital, a fellow Democrat is pressing for a measure to permit Mr. Emanuel’s recall from office. And here, demonstrators bearing thousands of signatures last week demanded Mr. Emanuel’s resignation, then blocked traffic on Christmas Eve along the city’s glittering North Michigan Avenue shopping district, chanting, “Rahm’s got to go in 2016!”

Since the release last month of video showing a white Chicago police officer firing 16 shots into a black teenager named Laquan McDonald, Mr. Emanuel has been a mayor under siege. A debate over race and policing has swept through many cities this year, but its arrival here has pointed an especially bright spotlight on City Hall. And the fatal shooting of two people by the police Saturday morning, one of them a 19-year-old man with possible mental health problems and the other a 55-year-old bystander, intensified the scrutiny. Mr. Emanuel, who is vacationing in Cuba, issued statements saying that the city was grieving, that the public deserved answers, and that officers’ training for handling mental health crises must be re-examined.

Even before this, Mr. Emanuel had a complicated, uncertain relationship with some of Chicago’s black residents over the closing of dozens of schools and a struggle to slow gang-related gun violence. Those issues helped force him into a difficult runoff election this year as he sought a second term as mayor.

Mr. Emanuel, a former congressman and chief of staff to President Obama, was known in Washington for his savvy in managing political crises, as well as a swaggering, often abrasive personal style. But recently he has been showing a more contrite side. Before he left for Cuba on what aides said was a long-planned family vacation, the mayor spent much time conferring with advisers, exchanging text messages with allies on the City Council, visiting local police stations and holding private meetings with African-American leaders like the Rev. Marshall E. Hatch, who met with Mr. Emanuel at a West Side church.