Larry Eichel, director of Pew's Philadelphia Research Initiative, said the school crisis had an impact on attitudes. "There's no question that it influenced the mood of the poll," he said.
That same poll also asked 1,605 city residents to rate the performance of the School District.
Those results, released last week, showed attitudes toward the schools suffering as well. Nearly half of those surveyed said the district's budget problems would cause families to abandon public schools.
Nutter has polled better in previous surveys with whites and higher-income residents, and that trend continued.
"It's just his approval ratings across all these groups dropped 20 points or so," Eichel said.
The poll did not ask those surveyed to explain their views about the mayor.
Mark McDonald, a spokesman for the mayor, said Nutter "shares the intense level of concern" residents have for the city.
"While the city has experienced a decline in violent crime and we're seeing plenty of evidence that the economy is improving, the public schools are the issue in the forefront of Philadelphians' concerns," he said.
McDonald listed a handful of the mayor's efforts in recent years to get new money for the schools, and cited Nutter's quest to secure a "sustainable funding stream" for schools from the state.
"The school funding issue is a solvable problem," McDonald said, "and he's working to stabilize School District finances."
Questions about the direction and overall state of the city also reflected the peculiar mixture of pessimism and pride inherent in many Philadelphians.
City residents were downbeat about the city's direction - 47 percent said the city was "on the wrong track," while 37 percent said it was "headed in the right direction."
The numbers of Philadelphians who thought the city would improve in the next five years also dropped from 68 percent to 52 percent.
Despite those gloomy results, 60 percent rated the city as a good or excellent place to live. Those numbers have fluctuated little over the five years of polling.
"We don't demand that respondents be consistent in their views," Eichel said.
The poll also continued to show the phenomenon of longer-term Philadelphia residents having a more grim outlook of the city's direction.
Geographically speaking, Northeast Philadelphia dominated in the pessimism department - 44 percent of residents there said the city was worse off than five years ago, compared with 37 percent citywide.
The poll was conducted between July 23 and Aug. 13. By then, elected officials had been battling for months over how to fill a $304 million hole in the School District budget - a problem that remains unsolved. On Aug. 8, School Superintendent William R. Hite Jr. said the district's money woes could threaten the start of the school year. Classes did eventually start on time.
The poll also came soon after the fatal building collapse on Market Street that raised questions about city oversight, and the enactment of a contentious property tax system.
The poll's overall margin of error was plus or minus 2.5 percentage points.
While Nutter fared poorly, Council members rated worse. While 30 percent of those polled approved of their job performance - down from 35 percent last year - 57 percent disapproved.
Jane Roh, a spokeswoman for Council President Darrell L. Clarke, said Council "understands the public's dissatisfaction" with the ongoing school crisis.
"No elected leader involved looks like a hero right now," she said. "But Council President Clarke and members of City Council will continue to press for sustainable and reliable funding for public schools that is fair to Philadelphia taxpayers."