For months, anger within the Democratic Party over President Biden’s support for Israel in the war in Gaza has been building. Protesters have shouted through his campaign events, marched outside the White House and vilified him as “Genocide Joe” on social media.

Now, Michigan’s primary election next week will put that discontent on the ballot for the first time, with Mr. Biden’s liberal detractors urging Democrats to vote “uncommitted” against him. Some of the president’s allies worry that a movement to register disapproval against him now could have lasting effects into the general election — especially if Mr. Biden does not alter his stance toward the conflict.

Michigan’s combination of an early primary, a large and politically active Arab American population, progressive students on college campuses and the option of a protest vote have raised the stakes of what has otherwise been a sleepy election in the state.

There are warning signs for Mr. Biden that frustration over Gaza has metastasized beyond Dearborn and other Detroit suburbs, which are the heart of Michigan’s Arab diaspora, and onto the state’s college campuses, where students increasingly feel affinity with the Palestinian cause.

In some Michigan communities without a large Arab American presence, crowds have demanded that their local governments enact cease-fire resolutions. Last week, The Detroit Metro Times, an alternative weekly newspaper, endorsed voting “uncommitted” in the primary.

There is no public polling to indicate how much support the “uncommitted” push might bleed from Mr. Biden, but Democrats at the highest levels of Michigan politics have cautioned — most of them privately — that the president is at risk of losing the state to former President Donald J. Trump if those who disagree with his Israel policy stay home or vote for a third-party candidate.