James was born in New Brunswick and attended Queen's College (now Rutgers University), graduating in 1775. When he graduated he raised a volunteer company in New Brunswick and led it as Captain in the Middlesex County militia. He led them in the Battle of Brooklyn on August 27, 1776 where he was captured. He was held as a prisoner of war until early in the spring of 1777 when he escaped to rejoin the Continental Army at Morristown.

Schureman returned to New Brunswick and took up a mercantile career while still serving in the militia. He was elected to the New Jersey State House of Assembley from 1783 to 1785. In 1786 New Jersey sent him as a delegate to the Continental Congress. That same year he was one of those at the Annapolis Convention that called for a new constitution for the United States. He continued in the Congressional session of 1787, then was returned to the state assembly in 1788.

When the United States was formed, Schureman was elected to the First House of Representatives, serving from 1789 until 1791. He served two other terms in the House (1797-1799) and (1813-1815). He was elected to the U.S. Senate to complete the term of John Rutherford and served there from 1799 to 1801. Between these duties he served a number of years as the Mayor of New Brunswick including 1792-1794, 1801-1813, and 1821-1824.

When Schureman died in 1824 at New Brunswick, he was buried in the Churchyard of the First Dutch Reformed Church there. The church and cemetery still stand and are located at Neilson and Bayard Streets.