Durkee was born in Royalton, Vermont. He became a merchant and moved to Wisconsin in 1836. There he became involved in agriculture and lumbering, and was a founder of the town of Southport (later Kenosha, Wisconsin). He entered politics, serving two terms in the territorial legislature. He became a member of the Free Soil Party and was elected to the United States House of Representatives in 1848 as part of Wisconsin's first full congressional delegation. He served in the House for two terms, until 1853. In 1854, he switched to the newly formed United States Republican Party and was elected to the United States Senate by the Wisconsin State Legislature. He served for one term, from 1855 to 1861. In 1865 he became governor of the Utah Territory, and served in that position until 1869 when he resigned because of ill health. He died in Nebraska while returning home.