Wurts was born in Flanders, New Jersey on August 13, 1792. After his father's death in 1793, the family relocated to Montville, New Jersey, and then relocated again, this time to Philadelphia, Pennsylvania. He graduated from Princeton College in 1813, studied law, was admitted to the bar in 1816, and began to practice law in Philadelphia.
Wurts was elected to the Nineteenth Congress, but was not a candidate for renomination. From 1827 to 1831, he served as a United States district attorney and was a member of the Philadelphia City Council.
Although he traveled abroad for his health in 1859, Wurts failed to recover and died in Rome in 1861. At the time of his death, Rome was under the direct rule of the Pope, with Italian unification not reaching completion until 1871. His remains were returned to the United States and interred in the family cemetery at Pleasant Mills, New Jersey, near Batsto, New Jersey.
