Mr. Little, a former mayor and state senator, beat two other candidates. He focused on promises of banning corporate money from politics and supporting Medicare for all.
Ms. Cooke, a three-time congressional candidate, held a huge fund-raising edge in a western Wisconsin race that Democrats consider pivotal to their hopes of flipping the House.
The small group of independent surveys in the Democratic primary for Senate and the Republican primary for governor showed a large share of undecided voters.