In 1791, he was chosen to represent the town of New Haven in the General Assembly (Connecticut State House of Representatives), and was annually re-elected for six years, until 1797, when he was chosen a member of the Connecticut State Council, or Upper House. Though one of the youngest members of the House, he soon became one of the most influential, and in 1794, three years after he entered it, he was chosen to preside over it as Speaker, at the age of 29. Daggett returned to the House for a one-year term in 1805.