LOS ANGELES — There are 900 schools, 30,000 teachers and more than 600,000 students in the Los Angeles public school system. By the end of the week, a teacher strike could throw them all into crisis.

After months of failed negotiations, teachers are expected to walk off the job on Thursday, in a show of frustration over what they say are untenable conditions in the second-largest school system in the country.

Teachers and other employees in the Los Angeles Unified School District are demanding higher pay, smaller class sizes and more support staff like counselors and librarians. But district officials say that they do not have the money to meet all of the demands and that the strike would do more damage to schools than good.

A strike in Los Angeles would offer a new stage for the national teacher protest movement, which in the last year has driven walkouts against stagnant pay and low education funding in six states. A walkout in staunchly liberal Los Angeles would also signal a major shift in a movement that has spread mostly in conservative or swing states with weaker unions.