Black voter turnout has declined in Wisconsin. Democrats see reversing that trend as key to Senate victory.

MILWAUKEE — After Mandela Barnes gave a brief but impassioned speech at a predominantly Black church here on a recent Sunday morning, parishioner Amber Smith said she was “very impressed.”

She said the Democratic candidate for the U.S. Senate gave “very strong remarks,” and she praised him for having spoken “with conviction.”

But Smith, a 30 year-old Milwaukee resident who works in higher education, signaled that she remained undecided on whether to vote for him — or whether to vote at all.

“I’m leaning toward it, but I need to...