Blaine County is a county in the U.S. state of Nebraska. As of the 2020 United States Census, the population was 431, making it Nebraska's second-least populous county and the sixth-least populous in the United States. Its county seat is Brewster. The county was formed in 1885 and organized in 1886. It is named after presidential candidate James G. …Blaine County is a county in the U.S. state of Nebraska. As of the 2020 United States Census, the population was 431, making it Nebraska's second-least populous county and the sixth-least populous in the United States. Its county seat is Brewster. The county was formed in 1885 and organized in 1886. It is named after presidential candidate James G. Blaine.