The school system, which employs about 25,000 teachers, announced contingency plans in the event of a strike, including a program to open 144 of its 675 schools with half-days of activities supervised by people other than unionized teachers. Officials said that program would also include meals — no small concern since 84 percent of the city’s public school students qualify for the free and reduced meals program.

Ms. Lewis deemed the contingency proposal, which was expected to be able to accommodate at least 150,000 students, “a mess,” and suggested that school officials were expecting families to “put their children with random folks.” For its part, the union on Saturday opened a strike headquarters where members could begin collecting picket signs and other materials to prepare for a walkout.

Negotiations have taken place behind closed doors since November, concerning wages and benefits, whether laid-off teachers should be considered for new openings, extra pay for those with more experience and higher degrees, and evaluations. District officials said the teachers’ average pay is $76,000 a year.

School officials, who say the system faces a $665 million deficit this year and a bigger one next year, have worked to cut costs even as Mr. Emanuel has pressed for what he considers much-needed “comprehensive reform,” including a longer school day.

Teachers have said they are being neglected on issues like promised raises, class sizes and support staff in the schools. By June, about 90 percent of teachers voted in favor of authorizing a strike if a new agreement could not be reached during the summer.

While negotiators handled the private talks, Chicagoans watched what appeared to be a contentious, sometimes personal fight between two blunt and resolute personalities: Mr. Emanuel and Ms. Lewis, who has described the mayor in recent days as a “bully” and a “liar,” and in a recent interview added, “I think the whole idea of an imperial mayoralty where you wave a magic wand or cuss someone out and things happen is untenable.”

Some parents said they were ultimately hopeful about the prospect of improvement in their children’s schools and eager for the changes advocated by Mr. Emanuel, whose own children attend private school. But others said that they thought teachers had been pushed hard, and that a standoff seemed inevitable.