He attended Newark Academy and Delaware College, and graduated from Yale College in 1861, where he was a member of Skull and Bones.
After studying law at the Harvard Law School, he was admitted to the bar in 1864 and began practice in Wilmington, Delaware. He also served for a time in the Union Army in 1864. Higgins was appointed deputy Attorney General in 1864 and was the United States attorney for Delaware from 1869 until 1876.
He was an unsuccessful Republican candidate for election to the 49th Congress in 1884, but was elected to the United States Senate and served from March 4, 1889 until March 3, 1895, when he unsuccessfully sought reelection.
Subsequently, he resumed the practice of law in Wilmington, including service as one of the attorneys for the respondent in the impeachment proceedings of United States District Court Judge Charles Swayne of Florida in 1904/05. Higgins died while at New York, New York, and is buried at the Saint Georges Cemetery, near Saint Georges in New Castle County.
Elections are held the first week of November. The General Assembly chose the United States. Senators, who took office March 4 for a six-year term.
He was a veteran of the Civil War and a member of the Republican, who served as United States Senator from Delaware. During his tenure he was Chairman of the Committee to Examine Branches of the Civil Service in the 51st and 52nd Congress, and a member of the Committee on Manufactures in the 52nd Congress.