Given the influence unions wield in the state, showing solidarity with workers is important for any Democrat who hopes to win California’s delegate-rich primary on Super Tuesday in March.

Thursday's debate, in fact, is only taking place at Loyola Marymount because the Democrats’ first choice as host, the University of California, Los Angeles, is enmeshed in a labor dispute of its own. The powerful AFSCME union has been battling the University of California system for three years over outsourcing on campuses and medical centers. Less than two weeks after announcing U.C.L.A. as the debate host in late October, party officials announced they were searching for a new location in the area and eventually relocated to Loyola Marymount, about 15 minutes away.

The debate will take place against the backdrop of a historic vote in the House, expected Wednesday, on whether to impeach President Trump. And it follows days of anxiety among Democrats about the dwindling number of participants on the stage. Of the seven candidates taking part— the smallest number yet for a debate — just one, Andrew Yang, will be a person of color. The leading black and Latino candidates failed to qualify, leading to concern that the debate field won’t be representative of the electorate that will choose a nominee.

The gathering will also reflect a new order in the party’s nominating contest. Mayor Pete Buttigieg of South Bend, Ind., after charging to a lead in Iowa polls, has found himself under attack from Mr. Sanders and Ms. Warren. Mr. Sanders has also seen his stock rise in recent weeks as Ms. Warren has lost ground. Center stage will be occupied, as it has throughout the fall, by former Vice President Joseph R. Biden Jr., who remains the leader in national polling.

So far this year, labor unions have largely stayed on the sidelines, waiting to see how the Democratic field shakes out. Only a few endorsements have been handed out as unions try to push candidates closer to their preferred positions, leading to a prolonged courtship throughout the year by the leading primary contenders.

Mr. Dreier, the Occidental professor, said he has not seen sentiments this supportive of labor unions from the Democratic field in decades, and on Monday called Unite Here’s threat a “shot across the bow” for both Loyola Marymount and other universities that contract with Sodexo.

“They’re using this as a test of their strength,” Mr. Dreier said of the union. “This is a big coup for national attention.”