WASHINGTON — The emails to Michelle Obama began flooding in minutes after she spoke out at an October rally in New Hampshire, her voice shaking, about Donald J. Trump’s treatment of women. Sexual assault victims recounted their trauma, fathers poured out anxieties about unhealthy influences on their sons, and a distraught parent agonized over how to explain rape to a 10-year-old.

The next morning in the East Wing, a first lady who had spent years in the White House staying away from politics sorted through a thick sheaf of printed messages — a selection of the 600 she had already received, an amount that would triple by the end of the day — and realized there was an unlikely finale for her.

Mrs. Obama had become the breakout voice of Campaign 2016.

Dismissed early on by critics as an angry black woman unsuited for the tradition-bound role of first lady, she has emerged this fall as Hillary Clinton’s most popular surrogate, with soaring approval ratings that cut across party lines. Reluctant at first to engage in partisan politics, and conflicted when her husband decided to seek the presidency, Mrs. Obama has, almost in spite of herself, evolved into a powerful presence on the campaign trail.

“She has ended up to be the most effective and reassuring antidote to Trump that we have, and the best at making that contrast,” said Jennifer Palmieri, Mrs. Clinton’s communications director.