For months, the Democratic establishment had issued increasingly dire warnings that Dr. Abdul El-Sayed, a progressive Michigan firebrand who had never won an election, would struggle to win a swing-state Senate seat that the party could not afford to lose.

The state’s governor, members of Congress and attorney general lined up behind his primary opponent, Representative Haley Stevens, a centrist from a swing district. They argued that she could win the kind of tough races that are a hallmark of this battleground state, where voters have twice voted for Donald J. Trump and twice voted for Ronald Reagan.

On Tuesday, a slim plurality of Democratic primary voters disagreed, betting with their hearts on a candidate whose fiercely progressive message had thrilled a coalition of younger and college-educated liberals.

Now, as he heads into the general election, Dr. El-Sayed’s candidacy will pose perhaps the most consequential challenge to the party’s ascendant progressive wing: Can an insurgent candidate, with unabashedly left-wing positions, win in a moderate state?

Dr. El-Sayed will offer the first general election test of the competing theories of electability that have been debated among Democrats for nearly a decade. Since Senator Bernie Sanders exploded onto the national stage in 2016, progressives have argued that their party’s path to victory runs through a populist economic agenda that can attract a broad coalition of working-class voters. Centrists have pushed back, saying such proposals alienate the moderate voters the party must sway to to win back areas where it has lost ground in recent years.

The narrow results hinted at the tough race ahead in November, when Dr. El- Sayed will face former Representative Mike Rogers, a Republican who left Congress in 2015. Dr. El-Sayed enters the general election without a strong mandate from Democrats, after more than half of primary voters cast ballots for other candidates. He performed best in wealthier, younger areas of the state, while Ms. Stevens did better in places with greater numbers of Black and working-class voters.