When President Biden made Michigan one of the first states on the Democratic Party’s presidential nominating calendar, he increased the political influence of a populous, diverse battleground state.

That decision over a year ago has led to the most significant test of Mr. Biden’s standing within his party since he was elected, as a push to protest his support for Israel threatens to upend what his allies had expected would be a straightforward primary campaign.

Mr. Biden is still widely expected to win Michigan’s Democratic primary election on Tuesday by a significant margin. But a homegrown campaign to persuade Michiganders to vote “uncommitted” will measure the resistance he faces among Arab Americans, young voters, progressives and other Democrats over his stance on the war in Gaza.

A high number of “uncommitted” votes would send a warning to his campaign nationally and set off alarms in Michigan, which he won in 2020 but where polls show weakness against former President Donald J. Trump. A low number, by contrast, would give Mr. Biden and his Democratic allies renewed faith that he can weather the tensions and focus on campaign priorities like the economy and abortion rights.

The absence of reliable public polling has left the outcome uncertain, and has helped turn the primary into a night that Mr. Biden’s allies are sweating.

“I am going to be looking at Democratic turnout, and it will tell me if I need to be worried,” Representative Haley Stevens of Michigan said in an interview on Monday. “We will know on Wednesday how deep this is.”