(CNN) -- Chicago teachers and administrators started talking again Monday, hours after the educators' union called a strike and school officials said they had nothing left to give.
Public school teachers launched their first strike in the city in 25 years Sunday night, saying they were close to a deal on pay but far apart on teacher evaluations, benefits and other issues.
The strike left about 350,000 students with an unscheduled day off, and left some parents scrambling for alternatives.
The school district opened 144 of its 578 schools for part of the day to provide a safe environment and meals to children in need. Dozens of churches and civic organizations stepped in to provide activities for the thousands of suddenly idle students. And police, expecting an uptick in trouble with more kids on the streets, pulled officers from desk duty to increase patrols.
The union that represents nearly 30,000 teachers and support staff in the nation's third-largest school district called the strike after negotiators failed to reach a contract agreement with school administrators despite 10 months of talks.
Mayor Rahm Emanuel said teachers were harming Chicago's children by striking.
"This is in my view a strike of choice, and it's the wrong choice for our children," he said. "Stay at the table. Finish it for our children."
He said negotiators had resolved all but two issues -- teacher evaluations and provisions dealing with jobs for laid-off teachers.
However, Chicago Teachers Union President Karen Lewis said teachers had no choice but to strike, despite "intense but productive" bargaining sessions.
The primary disagreement appears to be teacher job security in the wake of a new program that evaluates teachers based on students' standardized test scores. Chicago Teachers Union board member Jay Rehak called the idea "data-driven madness."
As many as 6,000 teachers could lose their jobs under the evaluation system, according to Lewis, who called the system "unacceptable." The mayor's office, the city of Chicago, and school officials have questioned that job loss figure.
"This is no way to measure the effectiveness of an educator," Lewis said Sunday. "Further, there are too many factors beyond our control which impact how well some students perform on standardized tests such as poverty, exposure to violence, homelessness, hunger and other social issues beyond our control."
Another sticking point is a "recall" policy that would put laid-off teachers in line for job openings at other schools within the district. Emanuel said such a policy, supported by the union, would take hiring decisions away from school principals and put them in the hands of central administrators and union leaders.
"Direction and dictation should not come out of downtown," the mayor said.
Teachers also want to block changes to their health benefits and win concessions on classroom conditions.
Pay is also an issue. However, the union said the two sides are close to a pay agreement after school officials offered a deal that would increase salaries 16% over four years. The average teacher salary in Chicago was $74,839 for the 2011-2012 school year, according to the district.
In addition to the pay increase, the offer includes paid maternity leave and short-term disability coverage. It would also freeze health care cost increases for two-thirds of the union's membership.
The high school day would also be shortened slightly, and teachers would be limited to teaching five classes, the district said.
The district's existing proposal would cost $400 million over four years, according to school board President David Vitale.
Chicago schools can't afford more concessions, Vitale said. "We have no more flexibility when it comes to finance," he told CNN on Monday.
At a midday news conference, Emanuel called the plan on the table an "honest compromise that respects our teachers, does right by our kids and is fair to our taxpayers."
Union officials have said they are puzzled by the stance of Emanuel, the city's Democratic mayor, whom they accused of going back on promises to teachers, police officers and other civil servants, according to teachers union board member Jay Rehak.
"He has definitely been a huge disappointment," Rehak said. "He has disrespected virtually every middle-class person in this city."
Sen. Dick Durbin, D-Illinois, said he had no solution for the crisis but urged a quick resolution.
"Both sides need to get back to the table as quickly as possible and really stay in there, negotiate through the night if necessary," he said Monday. "Get it over with quickly so that we can get these kids back in school."
About 50,000 Chicago students who attend charter schools are unaffected by the strike and will remain in class.
While keeping 144 of its schools open to provide a haven for part of the day, the school district urged parents "to first explore other options for their children."
"We know that a strike will put a strain on many families, and no one will be hurt more by a strike than our students," the district said on its website.
One of the organizations opening doors for students during the strike is Young Chicago Authors, which has a free program for part of the day for students in grades six through 12.
"In collaboration with core performance artists and special guests, young people will see the power of their voices in action through film, performance and discussion," the group said.
Still, some parents were concerned about what would happen to their children during the strike.
"If the kids are not in school, they're out getting into some kind of trouble ... when they should be in school, learning," said Shatara Scaggs, the mother of two children in kindergarten and first grade. "I think they should be in school getting an education. I don't think the teachers should be on strike."