Thousands of teachers in the nation's second-largest school district walked off the job Monday, launching a strike that left hundreds of thousands of students without instructors and several local and state leaders, some potentially eyeing 2020 presidential campaigns, navigating politically treacherous terrain as they balance the dueling interests of educators and district officials.

Schools remain open across the Los Angeles Unified School District, but some 30,000 members of the United Teachers Los Angeles are largely marching outside their buildings, demanding increased pay and smaller class sizes. The impasse – Los Angeles' first teacher strike since 1989 – comes following widespread demonstrations by instructors in multiple states last year that are strongly believed to have had an impact on elections in affected areas.

Senator Kamala Harris speaks with survivors of sexual assault and their supporters as they protest against Judge Brett Kavanaugh's nomination on Capitol Hill in Washington, DC, Sept. 28, 2018.(Saul Loeb/AFP/Getty Images) Senator Kamala Harris speaks with survivors of sexual assault and their supporters as they protest against Judge Brett Kavanaugh's nomination on Capitol Hill in Washington, DC, Sept. 28, 2018.

In California, where Los Angeles Mayor Eric Garcetti and Sen. Kamala Harris are among those considering 2020 presidential runs, there have already been a variety of responses to the situation, ranging from neutrality to support for the teachers.

In a statement Friday and in a video posted to his Twitter account Sunday evening, Garcetti, who has faced questions about the potential challenge of running the city remotely should he launch a presidential campaign, maintained a neutral position, conceding that teachers were justified in asking for "smaller classes, more support staff, and community schools," while also acknowledge the district must look out for its "fiscal health.

"I remain steadfast in my belief that there is common ground between both sides and that this common ground will be critical to a final agreement," Garcetti said in the statement, additionally urging in his video message that "all of our ideas and resources" be brought to the negotiating table.

Harris, D-Calif., who also continues to consider a presidential campaign, was direct in her support of the teachers Monday, offering specific endorsement of the demands for "improved student conditions, such as smaller class sizes and more counselors and librarians."

"Los Angeles teachers work day in and day out to inspire and educate the next generation of leaders. I'm standing in solidarity with them as they strike for improved student conditions, such as smaller class sizes and more counselors and librarians," Harris tweeted in part Monday, minutes after ABC News requested comment from the senator on the strike.

Large-scale teacher strikes occurred in numerous states in 2018, most notably in Arizona, Oklahoma and West Virginia where statewide demonstrations descended upon capitol buildings and lasted a week or longer. In the aftermath, record numbers of teachers ran for political office, seeking to influence future debate over their demands firsthand.

"Win or lose, we are creating a pipeline of educators to be part of the decision-making in places where people have been deciding on budgets, class size, and textbooks for years," Carrie Pugh, the National Education Association's political director told ABC News in April.

During his own campaign in 2018, newly inaugurated California Gov. Gavin Newsom outlined an education platform that included several areas of focus in common with United Teachers Los Angeles, such as expanding "full-service community schools" and taking steps to "attract and retain quality teachers."

California Gov. Gavin Newsom leaves the auditorium stage after presenting his first state budget during a news conference, Jan. 10, 2019, in Sacramento, Calif.(Rich Pedroncelli/AP) California Gov. Gavin Newsom leaves the auditorium stage after presenting his first state budget during a news conference, Jan. 10, 2019, in Sacramento, Calif.

Newsom, who was also believed to harbor presidential ambitions in the past, but said he would not run in 2020 during his gubernatorial campaign, specifically called for "supported and respected" during his inaugural address last week. The governor's press office did not immediately respond to ABC News's request for comment on the Los Angeles strike.

ABC News' Kendall Karson contributed to this report.