PEMBROKE PINES, Fla.—Rain poured down on Hillary Clinton and her supporters here, so the Democratic nominee cut her speech short and delivered what her campaign hopes will be an uplifting final message after a nasty, insult-driven campaign.

“Here’s what I want you to remember: I want to be the president for everybody,” she said as a driving rain picked up strength. “Let’s vote for the future! Let’s vote for what we want for our country.”

Her...