The progressive Laura Moser made the May 22 runoff despite a late attempt by the House Democratic campaign arm to derail her candidacy. Ms. Moser, an author and an organizer, trailed Lizzie Pannill Fletcher, a lawyer, but Ms. Fletcher failed to garner 50 percent of the vote, so they will face off again in a race that will be something of a proxy battle between the moderate and more liberal wings of the Democratic Party.