According to this story, some Nebraska legislators want to move the primary from May to April. There is no bill to make that change, but Senator John Murante already has an election law bill, LB 1048, and he may amend his bill to make the date change. Thanks to FrontloadingHQ for the news.
Nebraska’s primary has been in May since 1956. Before then, it was in April in presidential years and August in midterm years.