When Representative Elissa Slotkin of Michigan announced her candidacy for Senate early last year, Democrats had high hopes that her record as a defense hawk and centrist with proven cross-party appeal would make her an ideal candidate for keeping the swing-state seat in Democratic hands.

But now, Ms. Slotkin’s résumé and her pro-Israel record are threatening to become liabilities in a deadlocked race that could shift the balance of power in the Senate.

Michigan’s sizable contingent of Arab Americans has been directly affected by Israel’s military campaigns in Gaza and especially Lebanon. And in their grief and anger, some of these normally reliable Democratic voters are weighing withholding their support from Ms. Slotkin or sitting out the election altogether, potentially cutting into the margin she would need to win.

“This year, I’m not going to be voting,” Nina Saad, 49, said last week, as she sipped from a steaming demitasse cup of black coffee outside one of the Dearborn’s many cafes. Neither Ms. Slotkin nor her Republican opponent, former Representative Mike Rogers, she said, was offering a message that would motivate her to vote.

“Everybody’s taking the wrong position on what’s going on overseas,” Ms. Saad said of the candidates, adding that her friends and neighbors “all feel the same.”

The political stakes of the race could not be higher. Democrats are in an uphill fight to keep their majority in the Senate, which they currently hold by a mere two seats. In order to have any chance of maintaining control, they must not only defend incumbents in solidly red states including Montana and Ohio, but also hold onto seats in battleground states including Michigan, where the retirement of Senator Debbie Stabenow has left a seat up for grabs.